%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    %                                                               %
    %              tkz-berge.sty      encodage : utf8               %
    %                                                               %
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    %                                                               %
    %           Créé par Alain Matthes le 08-05-2007.               %
    %        contribution :  Rafael Villarroel 2007   (RV)          %
    %        contribution :  Rafael Villarroel 2009   (RV)          %
    %                                                               %
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    
    % modif Doyle form 1
    % add   \setkeys[GR]{edge}{#1}% in edge's macros
    % remove somme bugs with pgf 2.00 cvs
    
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%% Objet :  Création de graphes classiques
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{tkz-berge}[2011/06/01 2.00  tkz-berge for named graphs]

%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\RequirePackage{tkz-graph}
\def\tkzutil@empty{}
\def\tkzutil@firstofone#1{#1}
\def\tkzutil@firstoftwo#1#2{#1}
\def\tkzutil@secondoftwo#1#2{#2}
%<--------------------------------------------------------------------------–>
\long\def\tkzutil@ifundefined#1{%
  \expandafter\ifx\csname#1\endcsname\relax
    \expandafter\tkzutil@firstoftwo
  \else
    \expandafter\tkzutil@secondoftwo
  \fi}      
%\input{tkz-tools-arith.tex}
\tkzutil@ifundefined{pgfmath@function@isfactor}{%
   \pgfmathdeclarefunction{isfactor}{2}{%  
\begingroup 
\c@pgfmath@counta#1\relax%   
\c@pgfmath@countb#2\relax%   
\c@pgfmath@countc#1\relax%
\divide\c@pgfmath@counta by\c@pgfmath@countb%
\multiply\c@pgfmath@counta by\c@pgfmath@countb% 
\advance\c@pgfmath@countc by-\c@pgfmath@counta%
\ifnum\c@pgfmath@countc=0 \def\pgfmathresult{1}%
\else
  \def\pgfmathresult{0}%
  \fi
\pgfmath@smuggleone\pgfmathresult%
\endgroup} 
}{}  


\edef\tkzAtCode{\the\catcode`\@} 
\catcode`\@=11\relax  
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcounter{tkz@bg@cnt}    
%                             NAMED GRAPHS
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                         Graphes cls
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\define@cmdkey  [GR] {cl} {L}{}
\define@boolkey [GR] {cl} {Math}[true]{}
\define@boolkey [GR] {cl} {inv}[true]{}
\define@cmdkey  [GR] {cl} {RA}{}
\define@cmdkey  [GR] {cl} {RB}{}
\define@cmdkey  [GR] {cl} {RC}{}
\define@cmdkey  [GR] {cl} {RD}{}
\define@cmdkey  [GR] {cl} {RE}{}
\define@cmdkey  [GR] {cl} {RS}{}
\define@cmdkey  [GR] {cl} {prefix}{}
\define@cmdkey  [GR] {cl} {prefixx}{}
\define@cmdkey  [GR] {cl} {prefixxx}{}
\define@cmdkey  [GR] {cl} {prefixxxx}{}
\define@cmdkey  [GR] {cl} {prefixxxxx}{}
\define@cmdkey  [GR] {cl} {form}{}
\define@cmdkey  [GR] {cl} {num}{}
\define@cmdkey  [GR] {cl} {rotation}{}
\define@cmdkey  [GR] {cl} {x}{}
\define@cmdkey  [GR] {cl} {y}{}
\define@cmdkey  [GR] {cl} {r}{}
\define@cmdkey  [GR] {cl} {d}{}
\presetkeys     [GR] {cl} {RA         = 4,
                           RB         = 3,
                           RC         = 2,
                           RD         = 1,
                           RE         = 0.5,
                           RS         = 0,
                           form       = 1,
                           prefix     = a,
                           prefixx    = b,
                           prefixxx   = c,
                           prefixxxx  = d,
                           prefixxxxx = e,
                           num        = {},
                           Math       = false,
                           x          = 0,
                           y          = 0,
                           r          = 0,
                           d          = 0,
                           rotation   = 0}{}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                      Tools Graphes particuliers
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                           Some tools
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grMathSep}{_}
\newcommand*{\grLabelSep}{;}

\newcommand*{\write@math}[3]{%
            \Vertex[x = #1,y = #2,%
                    L = \cmdGR@cl@prefix\grMathSep{#3}]{\cmdGR@cl@prefix#3}}
\newcommand*{\write@nomath}[3]{%
            \Vertex[x = #1,y = #2]{\cmdGR@cl@prefix#3}}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                           Empty graphs
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grEmptyCycle}{\@ifstar%
                              \grEmptyCycleStar%
                              \grEmptyCycleNoStar}
\newcommand*{\grEmptyCycleNoStar}[2][]{%
  \begingroup%
  \setkeys[GR]{cl}{#1}%
  \pgfmathsetcounter{tkz@gr@p}{#2-1}
  \edef\tkz@auxctp{\thetkz@gr@p}
  \foreach \V@x in  {0,...,\tkz@auxctp}{%
    \pgfmathparse{360/#2*\V@x+\cmdGR@cl@rotation}
    \let\tkz@angle\pgfmathresult%
\pgfmathsetmacro{\x@result}{%
  \cmdGR@cl@RA*cos(\tkz@angle)+\cmdGR@cl@r*cos(\cmdGR@cl@d)}    
  \pgfmathsetmacro{\y@result}{%
  \cmdGR@cl@RA*sin(\tkz@angle)+\cmdGR@cl@r*sin(\cmdGR@cl@d)}
    \ifGR@cl@Math%
    \presetkeys [GR] {vertex} {Math = true}{}%
    \Vertex[x = \x@result+\cmdGR@cl@x,%
            y = \y@result+\cmdGR@cl@y,%
            L = \cmdGR@cl@prefix\grMathSep{\V@x}]{\cmdGR@cl@prefix\V@x}%
    \else%
    \Vertex[x = \x@result+\cmdGR@cl@x,%
            y = \y@result+\cmdGR@cl@y]{\cmdGR@cl@prefix\V@x}%
    \fi%
  }%
  \endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand{\grEmptyCycleStar}[2][]{%
  \begingroup%
  \setkeys[GR]{cl}{#1}%
  \setcounter{tkz@gr@a}{0} 
  \setcounter{tkz@gr@b}{0} 
  \foreach \V@x in {#2}{\stepcounter{tkz@gr@b}{1}}
  \foreach \V@x in {#2}{%
    \pgfmathsetmacro{\x@result}{%
      \cmdGR@cl@RA*cos((360/\thetkz@gr@b)*\thetkz@gr@a+\cmdGR@cl@rotation)%
      +\cmdGR@cl@r*cos(\cmdGR@cl@d)%
    }
    \pgfmathsetmacro{\y@result}{%
      \cmdGR@cl@RA*sin((360/\thetkz@gr@b)*\thetkz@gr@a+\cmdGR@cl@rotation)%
      +\cmdGR@cl@r*sin(\cmdGR@cl@d)%
    }
    \ifGR@cl@Math%
    \Vertex[%
    x=\x@result+\cmdGR@cl@x,
    y=\y@result+\cmdGR@cl@y,
    L=$\V@x$]{\cmdGR@cl@prefix\thetkz@gr@a}%
    \else%
    \Vertex[%
    x=\x@result+\cmdGR@cl@x,
    y=\y@result+\cmdGR@cl@y,
    L=\V@x]{\cmdGR@cl@prefix\thetkz@gr@a}%
    \fi%
    \stepcounter{tkz@gr@a}%
  }
    \endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                         grEmptyPath  from (RV)
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grEmptyPath}{\@ifstar%
                              \grEmptyPathStar%
                             \grEmptyPathNoStar}
\newcommand*{\grEmptyPathNoStar}[2][]{%
\begingroup%
\setkeys[GR]{cl}{#1}%
\pgfmathsetcounter{tkz@gr@a}{#2-1}
\edef\tkz@auxctp{\thetkz@gr@a}
 \ifcase\cmdGR@cl@form
\or
\def\tkzb@result{0}
\foreach \V@x in  {0,...,\tkz@auxctp}{%
   \pgfmathsetmacro{\x@result}{\cmdGR@cl@RA*(\V@x)*cos(\cmdGR@cl@rotation)}
   \pgfmathsetmacro{\y@result}{\cmdGR@cl@RA*(\V@x)*sin(\cmdGR@cl@rotation)}
 \pgfmathsetmacro{\x@coord}{\x@result+\cmdGR@cl@x+\cmdGR@cl@r*cos(\cmdGR@cl@d)}
 \pgfmathsetmacro{\y@coord}{\y@result+\cmdGR@cl@y+
 \cmdGR@cl@r*sin(\cmdGR@cl@d)+\cmdGR@cl@RS}
  \ifGR@cl@Math%
        \presetkeys [GR] {vertex} {Math = true}{}%
        \ifthenelse{\equal{\cmdGR@cl@num}{}}{%
          \write@math{\x@coord}{\y@coord}{\V@x}}{%
          \write@math{\x@coord}{\y@coord}{\V@x\grLabelSep\cmdGR@cl@num}}%
         \else
           \ifthenelse{\equal{\cmdGR@cl@num}{}}{%
             \write@nomath{\x@coord}{\y@coord}{\V@x}}{%
             \write@nomath{\x@coord+\cmdGR@cl@x}{\y@coord}{%
                            \V@x\grLabelSep\cmdGR@cl@num}}%
        \fi}%
 \or
\foreach \V@x in  {0,...,\tkz@auxctp}{%
  \pgfmathsetmacro{\x@result}{%
      \cmdGR@cl@RA*(2*\V@x-\thetkz@gr@a)*0.5*cos(\cmdGR@cl@rotation)}
  \pgfmathsetmacro{\y@result}{%
      \cmdGR@cl@RA*(2*\V@x-\thetkz@gr@a)*0.5*sin(\cmdGR@cl@rotation)}
  \pgfmathsetmacro{\x@coord}{%
                \x@result+\cmdGR@cl@x+\cmdGR@cl@r*cos(\cmdGR@cl@d)}
  \pgfmathsetmacro{\y@coord}{%
         \y@result+\cmdGR@cl@y+\cmdGR@cl@r*sin(\cmdGR@cl@d)+\cmdGR@cl@RS}
  \ifGR@cl@Math%
     \presetkeys [GR] {vertex} {Math = true}{}%
     \ifthenelse{\equal{\cmdGR@cl@num}{}}{%
          \write@math{\x@coord}{\y@coord}{\V@x}}{%
          \write@math{\x@coord}{\y@coord}{\cmdGR@cl@num\grLabelSep\V@x}}%
  \else
    \ifthenelse{\equal{\cmdGR@cl@num}{}}{%
             \write@nomath{\x@coord}{\y@coord}{\V@x}}{%
             \write@nomath{\x@coord}{\y@coord}{\cmdGR@cl@num\grLabelSep\V@x}}%
  \fi
}%
\fi
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand{\grEmptyPathStar}[2][]{%
\begingroup%
  \setkeys[GR]{cl}{#1}%
  \setcounter{tkz@gr@a}{0} 
  \ifcase\cmdGR@cl@form
  \or
  % form 1
  \foreach \V@x in {#2}{%
    \pgfmathsetmacro{\x@result}{\cmdGR@cl@RA*\value{tkz@gr@a}*cos(\cmdGR@cl@rotation)%
      +\cmdGR@cl@r*cos(\cmdGR@cl@d)}%
    \pgfmathsetmacro{\y@result}{\cmdGR@cl@RA*\value{tkz@gr@a}*sin(\cmdGR@cl@rotation)%
      +\cmdGR@cl@r*sin(\cmdGR@cl@d)}%
    \ifGR@cl@Math%
    \Vertex[%
    x=\x@result+\cmdGR@cl@x,
    y=\y@result+\cmdGR@cl@y,
    L=$\V@x$]{\cmdGR@cl@prefix\thetkz@gr@a}%
    \else%
    \Vertex[%
    x=\x@result+\cmdGR@cl@x,
    y=\y@result+\cmdGR@cl@y,
    L=\V@x]{\cmdGR@cl@prefix\thetkz@gr@a}%
    \fi%
    \stepcounter{tkz@gr@a}%
  }%
  \or
  % form 2
  \setcounter{tkz@gr@a}{0} 
  \setcounter{tkz@gr@b}{0} 
  \foreach \V@x in {#2}{\stepcounter{tkz@gr@b}{1}}
  \foreach \V@x in {#2}{%
    \pgfmathsetmacro{\x@result}{\cmdGR@cl@RA*(2*\value{tkz@gr@a}-\value{tkz@gr@b}+1)*0.5%
      *cos(\cmdGR@cl@rotation)%
      +\cmdGR@cl@r*cos(\cmdGR@cl@d)%
    }
    \pgfmathsetmacro{\y@result}{\cmdGR@cl@RA*(2*\value{tkz@gr@a}-\value{tkz@gr@b}+1)*0.5%
      *sin(\cmdGR@cl@rotation)%
      +\cmdGR@cl@r*sin(\cmdGR@cl@d)%
    }
    \ifGR@cl@Math%
    \Vertex[%
    x=\x@result+\cmdGR@cl@x,
    y=\y@result+\cmdGR@cl@y,
    L=$\V@x$]{\cmdGR@cl@prefix\thetkz@gr@a}%
    \else%
    \Vertex[%
    x=\x@result+\cmdGR@cl@x,
    y=\y@result+\cmdGR@cl@y,
    L=\V@x]{\cmdGR@cl@prefix\thetkz@gr@a}%
    \fi%
    \stepcounter{tkz@gr@a}
  }
  \fi
  \endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                                 grEmptyStar
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grEmptyStar}[2][]{%
\begingroup%
   \setkeys[GR]{cl}{#1}%
   \pgfmathsetcounter{tkz@gr@a}{#2-1}
   \ifGR@cl@Math\presetkeys [GR] {vertex} {Math = true}{}%
     \write@math{0}{0}{\thetkz@gr@a}%
   \else
     \write@nomath{0}{0}{\thetkz@gr@a}%
   \fi
   \grEmptyCycle[#1]{\thetkz@gr@a}
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                               grEmptyGrid
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand{\grEmptyGrid}[3][]{%
\begingroup%
   \setkeys[GR]{cl}{#1}%
   \pgfmathsetcounter{tkz@gr@a}{#2-1}
       \edef\tkz@auxctpa{\thetkz@gr@a}
   \pgfmathsetcounter{tkz@gr@b}{#3-1}
       \edef\tkz@auxctpb{\thetkz@gr@b}
   \foreach \V@x in {0,...,\tkz@auxctpa}{%
      \foreach \V@y in {0,...,\tkz@auxctpb}{%
      \ifGR@cl@Math\presetkeys [GR] {vertex} {Math = true}{}%
         \write@math{\cmdGR@cl@RA*\V@x}{\cmdGR@cl@RB*\V@y}{\V@x\grLabelSep\V@y}%
      \else
         \write@nomath{\cmdGR@cl@RA*\V@x}{\cmdGR@cl@RB*\V@y}{\V@x\grLabelSep\V@y}%
      \fi}%
   }
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                             grEmptyLadder
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grEmptyLadder}[2][]{%
\begingroup%
  \setkeys[GR]{cl}{#1}%
  \grEmptyPath[#1,RS=0]{#2}
  \edef\tkzb@ptemp{\cmdGR@cl@prefixx}
  \edef\tkzb@rtemp{\cmdGR@cl@RB}
  \grEmptyPath[#1,prefix=\tkzb@ptemp,RS=\tkzb@rtemp]{#2}
\endgroup%
}


%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                                 Edges 
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\EdgeInGraphFromOneToComp}[4][]{% #4 
\begingroup%
  \setkeys[GR]{edge}{#1}%
   \pgfmathsetcounter{tkz@gr@ta}{#3-1}
       \edef\tkz@auxctp{\thetkz@gr@ta}
   \foreach \cx in  {0,...,\tkz@auxctp}{%
        \ifthenelse{\equal{\cx}{#4}}{}{\Edge[#1](#2#4)(#2\cx)}%
        }%
\endgroup%
}

%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% new tool EdgeInGraphLoop loop 0--1--2.........n--0
% star 0--1--2.........n-
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\EdgeInGraphLoop}{\@ifstar%
                              \EdgeInGraphLoopStar%
                              \EdgeInGraphLoopNoStar}
\newcommand*{\EdgeInGraphLoopNoStar}[3][]{% #4 
\begingroup%
\setkeys[GR]{edge}{#1}%
    \pgfmathsetcounter{tkz@gr@ta}{#3-1}
    \setcounter{tkz@gr@n}{0}
    \Edge[#1](#2\thetkz@gr@ta)(#2\thetkz@gr@n)
    \pgfmathaddtocounter{tkz@gr@ta}{-1}
    \edef\tkz@auxctp{\thetkz@gr@ta}
        \foreach \V@x in  {0,...,\tkz@auxctp}{%
        \stepcounter{tkz@gr@n}
        \Edge[#1](#2\V@x)(#2\thetkz@gr@n)%
       }%
\endgroup%
}
\newcommand*{\EdgeInGraphLoopStar}[3][]{% #4 
\begingroup%
\setkeys[GR]{edge}{#1}%
    \pgfmathsetcounter{tkz@gr@ta}{#3-2}
    \setcounter{tkz@gr@n}{0}
    \edef\tkz@auxctp{\thetkz@gr@ta}
        \foreach \V@x in  {0,...,\tkz@auxctp}{%
         \stepcounter{tkz@gr@n}
         \Edge[#1](#2\V@x)(#2\thetkz@gr@n)%
        }%
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% new tool EdgeInGraphMod replace nextmod
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\EdgeInGraphMod}{\@ifstar%
                              \EdgeInGraphModStar%
                              \EdgeInGraphModNoStar}
\newcommand*{\EdgeInGraphModNoStar}[4][]{% #2 order
\begingroup%
  \setkeys[GR]{edge}{#1}%
    \pgfmathsetcounter{tkz@gr@ta}{#3-1}
           \edef\tkz@auxctp{\thetkz@gr@ta}
    \foreach \V@x in  {0,...,\tkz@auxctp}{%
        \pgfmathsetcounter{tkz@gr@tb}{Mod(\V@x+#4,#3)}
        \Edge[#1](#2\thetkz@gr@tb)(#2\V@x)%
        }%
\endgroup%
}
%#1 prefix #2 order #3 add #4 start #5 décalage
\newcommand*{\EdgeInGraphModStar}[6][]{% 
\begingroup%
 \setkeys[GR]{edge}{#1}%
 \pgfmathsetcounter{tkz@gr@ta}{#5}
  \whiledo{\value{tkz@gr@ta}<#3}{%
     \pgfmathsetcounter{tkz@gr@n}{Mod(\thetkz@gr@ta+#4,#3)}
     \Edge[#1](#2\thetkz@gr@ta)(#2\thetkz@gr@n)
     \pgfmathaddtocounter{tkz@gr@ta}{#6}%
    }%
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%             EdgeInGraphModLoop dep #4 add #3 mod #2 until #4
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>

\newcommand*{\EdgeInGraphModLoop}[5][]{% #2 order
\begingroup%
  \setkeys[GR]{edge}{#1}%
    \setcounter{tkz@gr@ta}{#5}
    \setcounter{tkz@gr@n}{#3}
    \whiledo{\not\equal{\value{tkz@gr@n}}{#5}}{%
        \pgfmathsetcounter{tkz@gr@n}{Mod(\thetkz@gr@ta+#4,#3)}
        \Edge[#1](#2\thetkz@gr@ta)(#2\thetkz@gr@n)%
        \setcounter{tkz@gr@ta}{\thetkz@gr@n}
        }%
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                               EdgeIdentity
%  la version étoilée permet d'utliser une sélection
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\EdgeIdentity}{\@ifstar%
                              \EdgeIdentityStar%
                              \EdgeIdentityNoStar}
\newcommand*{\EdgeIdentityNoStar}[4][]{%
\begingroup%
  \setkeys[GR]{edge}{#1}%
 \pgfmathsetcounter{tkz@gr@e}{#4-1}
       \edef\tkz@auxctp{\thetkz@gr@e}
    \foreach \V@x in  {0,...,\tkz@auxctp}{%
       \Edge[#1](#2\V@x)(#3\V@x)%
       }%
\endgroup%
}
\newcommand*{\EdgeIdentityStar}[4][]{%
\begingroup%
  \setkeys[GR]{edge}{#1}%
    \foreach \V@x in  {#4}{%
       \Edge[#1](#2\V@x)(#3\V@x)%
       }%
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%  EdgeFromOneToAll  vertex #1#3 through #2 0...#2 n-1 #5 order of the graph
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\EdgeFromOneToAll}[5][]{% #4  = order of the graph
\begingroup%
  \setkeys[GR]{edge}{#1}%
     \pgfmathsetcounter{tkz@gr@e}{#5-1}
      \edef\tkz@auxctp{\thetkz@gr@e}
     \foreach \V@x in  {0,...,\tkz@auxctp}{%
        \Edge[#1](#2#4)(#3\V@x)%
        }%
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%  EdgeFromOneToSeq  vertex #1#3 through #2#4...#2#5
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\EdgeFromOneToSeq}[6][]{% #4 
\begingroup%
  \setkeys[GR]{edge}{#1}%
    \foreach \V@x in  {#5,...,#6}{%
        \Edge[#1](#2#4)(#3\V@x)%
        }%
\endgroup%
} %<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%  EdgeFromOneToSel vertex #1#3 through #2#4...#2#5
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\EdgeFromOneToSel}[5][]{% #4 
\begingroup%
  \setkeys[GR]{edge}{#1}%
    \foreach \V@x in  {#5}{%
        \Edge[#1](#2#4)(#3\V@x)%
        }%
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%  EdgeFromOneToComplement  vertex #1#3 through #2#4...#2#5
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\EdgeFromOneToComp}[5][]{%
\begingroup%
  \setkeys[GR]{edge}{#1}%
   \pgfmathsetcounter{tkz@gr@e}{#5-1}
    \edef\tkz@auxctp{\thetkz@gr@e}
   \foreach \cx in  {0,...,\tkz@auxctp}{%
        \ifthenelse{\equal{\cx}{#4}}{}{\Edge[#1](#2#4)(#3\cx)}%
        }%
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% new tool EdgeMod replace nextmod
% identity with step like nextmod ???
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\EdgeMod}{\@ifstar%
                                 \EdgeModStar%
                                 \EdgeModNoStar}
\newcommand*{\EdgeModNoStar}[5][]{%#3 order #4 step
\begingroup%
  \setkeys[GR]{edge}{#1}%
    \pgfmathsetcounter{tkz@gr@e}{#4-1}
           \edef\tkz@auxctp{\thetkz@gr@e}
    \foreach \V@x in  {0,...,\tkz@auxctp}{%
        \pgfmathsetcounter{tkz@gr@tb}{Mod(\V@x+#5,#4)}
        \Edge[#1](#2\V@x)(#3\thetkz@gr@tb)%
        }%
\endgroup%
}
%#1 prefix #2 prefix #3 order #4 order inf #5 step
\newcommand*{\EdgeModStar}[6][]{%
\begingroup%
  \setkeys[GR]{edge}{#1}%
     \setcounter{tkz@gr@ta}{0}
     \whiledo{\value{tkz@gr@ta}<#4}{%
        \pgfmathsetcounter{tkz@gr@tb}{Mod(\thetkz@gr@ta+#5,#4)}
        \Edge[#1](#2\thetkz@gr@ta)(#3\thetkz@gr@tb)%
        \pgfmathaddtocounter{tkz@gr@ta}{#6}}%
\endgroup%
}%
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% new tool EdgeInGraphSeq sequence  i--i+1--.....--j
% or i--i+k--...--j
% #1 options #2  graph #3   from #4 to
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\EdgeInGraphSeq}[4][]{% #4 
\begingroup%
\setkeys[GR]{edge}{#1}%
    \foreach \V@x in  {#3,...,#4}{%
      \pgfmathsetcounter{tkz@gr@n}{\V@x+1}
      \Edge[#1](#2\V@x)(#2\thetkz@gr@n)}%
\endgroup%
}%

%%%%%%%%%%% NEW COMMANDS
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% new tool EdgeSeq sequence  
% #1 options #2 first graph #3 second graph  #4 from #5 to
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand{\EdgeSequence}[5][]{%
\begingroup%
\setkeys[GR]{edge}{#1}%
  \foreach \V@x in  {#4,...,#5}{%
    \pgfmathsetcounter{tkz@gr@n}{\V@x+1}
    \Edge[#1](#2\V@x)(#3\thetkz@gr@n)}%
\endgroup% 
}%
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                     EdgeDoubleMod by RV
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\EdgeDoubleMod}[9]{%
\begingroup%
   \foreach \V@x in {0,...,#9}{%
      \pgfmathsetcounter{tkz@gr@c}{Mod(#3+(#4*\V@x),#2)}
      \pgfmathsetcounter{tkz@gr@n}{Mod(#7+(#8*\V@x),#6)}
      \Edge(#1\thetkz@gr@c)(#5\thetkz@gr@n)
    }%
\endgroup%
}

%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                     grPath
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grPath}[2][]{%
\begingroup%
    \setkeys[GR]{cl}{#1}%
     \grEmptyPath[#1]{#2}
    \ifthenelse{\equal{\cmdGR@cl@num}{}}{%
  \ifthenelse{\equal{#2}{1}}{}{%
      \EdgeInGraphLoop*{\cmdGR@cl@prefix}{#2}%
      }}{%
         \ifthenelse{\equal{#2}{1}}{}{%
        \ifcase\cmdGR@cl@form
        \or
          \pgfmathsetcounter{tkz@gr@ta}{#2-2}
          \setcounter{tkz@gr@n}{0}
             \edef\tkz@auxctp{\thetkz@gr@ta}
          \foreach \V@x in  {0,...,\tkz@auxctp}{%
              \stepcounter{tkz@gr@n}
              \Edge(\cmdGR@cl@prefix\V@x\grLabelSep\cmdGR@cl@num)%
                   (\cmdGR@cl@prefix\thetkz@gr@n\grLabelSep\cmdGR@cl@num)%
              }%
           \or
          \EdgeInGraphLoop*{\cmdGR@cl@prefix\cmdGR@cl@num\grLabelSep}{#2}
          \fi%
 }}
\endgroup%
}

%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                     grGrid
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grGrid}[3][]{%
\begingroup%
  \setkeys[GR]{cl}{#1}%
   \grEmptyGrid[#1]{#2}{#3}
   \pgfmathsetcounter{tkz@gr@a}{#2-2}
          \edef\tkz@auxctpa{\thetkz@gr@a}
   \pgfmathsetcounter{tkz@gr@b}{#3-2}
          \edef\tkz@auxctpb{\thetkz@gr@b}
   \foreach \V@x in {0,...,\tkz@auxctpa}{%
       \foreach \V@y in {0,...,\tkz@auxctpb}{%
          \pgfmathsetcounter{tkz@gr@c}{\V@x+1}
          \pgfmathsetcounter{tkz@gr@d}{\V@y+1}
          \Edge(\cmdGR@cl@prefix\V@x\grLabelSep\V@y)%
               (\cmdGR@cl@prefix\V@x\grLabelSep\thetkz@gr@d)
          \Edge(\cmdGR@cl@prefix\V@x\grLabelSep\V@y)%
               (\cmdGR@cl@prefix\thetkz@gr@c\grLabelSep\V@y)%
          }%
      }%
   \pgfmathsetcounter{tkz@gr@a}{#2-2}
   \pgfmathsetcounter{tkz@gr@b}{#3-1}
             \edef\tkz@auxctpa{\thetkz@gr@a}
  \foreach \V@x in {0,...,\tkz@auxctpa}{%
      \pgfmathsetcounter{tkz@gr@c}{\V@x+1}
      \Edge(\cmdGR@cl@prefix\V@x\grLabelSep\thetkz@gr@b)%
           (\cmdGR@cl@prefix\thetkz@gr@c\grLabelSep\thetkz@gr@b)%
      }%
   \pgfmathsetcounter{tkz@gr@a}{#2-1}
   \pgfmathsetcounter{tkz@gr@b}{#3-2}
               \edef\tkz@auxctpb{\thetkz@gr@b}
  \foreach \V@y in {0,...,\tkz@auxctpb}{%
      \pgfmathsetcounter{tkz@gr@d}{\V@y+1}
      \Edge(\cmdGR@cl@prefix\thetkz@gr@a\grLabelSep\V@y)%
           (\cmdGR@cl@prefix\thetkz@gr@a\grLabelSep\thetkz@gr@d)%
   }%
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                             grComplete  
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grComplete}[2][]{% #1 options #2 ordre du graphe
\begingroup%
  \setkeys[GR]{cl}{#1}%
  \grEmptyCycle[#1]{#2}%
  \pgfmathsetcounter{tkz@gr@a}{#2-1}
              \edef\tkz@auxctp{\thetkz@gr@a}
  \foreach \ia in {0,...,\tkz@auxctp}%
     {\foreach \ib in {\ia,...,\tkz@auxctp}
     {\Edge(\cmdGR@cl@prefix\ia)(\cmdGR@cl@prefix\ib)}%
      }%
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                               grCycle
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grCycle}[2][]{%
\begingroup%
  \setkeys[GR]{cl}{#1}
  \grEmptyCycle[#1]{#2}
  \EdgeInGraphLoop{\cmdGR@cl@prefix}{#2}
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                               grLCF
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand{\grLCF}[3][]{%
\begingroup%
   \setkeys[GR]{cl}{#1}%
   \setcounter{tkz@gr@a}{#3}
   \setcounter{tkz@gr@b}{0} 
   \foreach \V@x in {#2}{\stepcounter{tkz@gr@b}}
   \pgfmathsetcounter{tkz@gr@c}{\thetkz@gr@a * \thetkz@gr@b}
   \setcounter{tkz@gr@b}{\thetkz@gr@c}
   \grCycle[#1]{\thetkz@gr@c}
%<––––––––––––––––––––––––– End   Vertex ––––––––––––––––––––––––––––––––––––>
   \pgfmathsetcounter{tkz@gr@a}{#3-1}
    \edef\tkz@auxctp{\thetkz@gr@a}
   \setcounter{tkz@gr@e}{0}
   \foreach \V@k in  {0,...,\tkz@auxctp}{%
     \foreach \n in  {#2}{%
         \ifthenelse{\n < 0}{%
            \pgfmathsetcounter{tkz@gr@b}{\n+\thetkz@gr@c}}{%
            \pgfmathsetcounter{tkz@gr@b}{\n}}
         \pgfmathsetcounter{tkz@gr@n}%
                           {Mod(\thetkz@gr@e+\thetkz@gr@b,\thetkz@gr@c)}
         \Edge(\cmdGR@cl@prefix\thetkz@gr@e)(\cmdGR@cl@prefix\thetkz@gr@n)
         \stepcounter{tkz@gr@e}%
         }%
      }%
\endgroup%
}

%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                                 grStar
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grStar}[2][]{%
\begingroup%
   \setkeys[GR]{cl}{#1}%
   \grEmptyStar[#1]{#2}
   \pgfmathsetcounter{tkz@gr@p}{#2-1}
   \EdgeInGraphFromOneToComp{\cmdGR@cl@prefix}{#2}{\thetkz@gr@p}
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                                 grWheel
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grWheel}[2][]{
\begingroup%
    \setkeys[GR]{cl}{#1}%
    \grStar[#1]{#2}
    \pgfmathsetcounter{tkz@gr@e}{#2-1}
    \EdgeInGraphLoop{\cmdGR@cl@prefix}{\thetkz@gr@e}
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                                grSQCircle
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grSQCycle}[2][]{%
\begingroup%
    \setkeys[GR]{cl}{#1}%
    \grCycle[#1]{#2}%
    \EdgeInGraphMod{\cmdGR@cl@prefix}{#2}{2}
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                             grLadder
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grLadder}[2][]{%
\begingroup%
  \setkeys[GR]{cl}{#1}%
  \grPath[#1,RS=0]{#2}
  \edef\tkzb@ptemp{\cmdGR@cl@prefixx}
  \edef\tkzb@rtemp{\cmdGR@cl@RS}
  \grPath[#1,prefix=\tkzb@ptemp,RS=\tkzb@rtemp]{#2}
  \EdgeIdentity{\cmdGR@cl@prefix}{\cmdGR@cl@prefixx}{#2}
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                                 grPrism
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grPrism}[2][]{%
\begingroup%
    \setkeys[GR]{cl}{#1}%
        \grCycle[#1]{#2}
        \edef\tkzb@rtemp{\cmdGR@cl@RB}
        \edef\tkzb@ptemp{\cmdGR@cl@prefixx}
        \grCycle[#1,RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{#2}
      \EdgeIdentity{\cmdGR@cl@prefix}{\cmdGR@cl@prefixx}{#2}
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                                 grCompleteBipartite 
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grCompleteBipartite}[3][]{%
\begingroup%
  \setkeys[GR]{cl}{#1}%
  \pgfmathsetcounter{tkz@gr@a}{#2-1} 
  \pgfmathparse{(\cmdGR@cl@RA * \thetkz@gr@a) /2}
  \let\tkzRAxpos\pgfmathresult%
  \pgfmathsetcounter{tkz@gr@a}{#3-1} 
  \pgfmathparse{(\cmdGR@cl@RB * \thetkz@gr@a) /2}
 \let\tkzRBxpos\pgfmathresult%
  \ifdim\tkzRBxpos pt > \tkzRAxpos pt\relax%
   \pgfmathadd{\tkzRBxpos}{-\tkzRAxpos}
   \let\tkzaxpos\pgfmathresult%
   \def\tkzbxpos{0}
   \else%
    \pgfmathadd{\tkzRAxpos}{-\tkzRBxpos}
    \let\tkzbxpos\pgfmathresult%
    \def\tkzaxpos{0}
   \fi%
   \begin{scope}[xshift=\tkzaxpos cm]
     \grEmptyPath[#1,RS=0]{#2}
   \end{scope}
   \begin{scope}[xshift=\tkzbxpos cm]
     \edef\tkzb@ptemp{\cmdGR@cl@prefixx}
     \edef\tkzb@rtemp{\cmdGR@cl@RS}
     \edef\tkzb@stemp{\cmdGR@cl@RB}
     \grEmptyPath[#1,RA=\tkzb@stemp,prefix=\tkzb@ptemp,RS=\tkzb@rtemp]{#3}
   \end{scope}
   \pgfmathsetcounter{tkz@gr@p}{#2-1}
   \pgfmathsetcounter{tkz@gr@e}{#3-1}
   \edef\tkz@auxctp{\thetkz@gr@e}
   \foreach \cpx in {0,...,\tkz@auxctp}{%
     \EdgeFromOneToAll{\cmdGR@cl@prefixx}{\cmdGR@cl@prefix}{\cpx}{#2}
     }%
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                                 grTriangularGrid 
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grTriangularGrid}[2][]{%
\begingroup%
    \setkeys[GR]{cl}{#1}
    \ifcase\cmdGR@cl@form
      \or
%<––––––––––––––––––––– form 1 equilateral triangle ––––––––––––––––––––––––>
     \pgfmathsetcounter{tkz@gr@a}{#2-1}
     %\pgfmathsetcounter{tkz@gr@b}{#2}
     \edef\tkz@auxctp{\thetkz@gr@a}
     \foreach \lg in {0,...,\tkz@auxctp}{%
        \pgfmathsetcounter{tkz@gr@b}{#2-\lg}
        \setcounter{tkz@gr@b}{\thetkz@gr@b}
        \edef\tkzb@rtemp{\cmdGR@cl@RA}
        \edef\tkzb@ptemp{\cmdGR@cl@prefix}
        \pgfmathmultiply{\cmdGR@cl@RA}{\lg}
        \let\myresult\pgfmathresult
        \pgfmathparse{\cmdGR@cl@RA*\lg/2}
        \let\tkzaxpos\pgfmathresult
        \begin{scope}[xshift=\tkzaxpos cm]
           \grPath[#1,%
                   RA     = \tkzb@rtemp,%
                   RS     = \myresult,%
                   prefix = \tkzb@ptemp,%
                   num    = \lg]{\thetkz@gr@b}%
        \end{scope}%
     }
    \or
%<––––––––––––––––––––––––––– form 2 right triangle ––––––––––––––––––––––––>
    \pgfmathsetcounter{tkz@gr@a}{#2-1}
   % \pgfmathsetcounter{tkz@gr@b}{#2}
    \edef\tkz@auxctp{\thetkz@gr@a}
    \foreach \lg in {0,...,\tkz@auxctp}{%
       \pgfmathsetcounter{tkz@gr@b}{#2-\lg}
       \setcounter{tkz@gr@b}{\thetkz@gr@b}
       \edef\tkzb@rtemp{\cmdGR@cl@RA}
       \edef\tkzb@ptemp{\cmdGR@cl@prefix}
       \pgfmathmultiply{\cmdGR@cl@RA}{\lg}
       \let\myresult\pgfmathresult
       \grPath[#1,%
               RA     = \tkzb@rtemp,%
               RS     = \myresult,%
               prefix = \tkzb@ptemp,%
               num    = \lg,form=1]{\thetkz@gr@b}%
    }
    \or
     \pgfmathsetcounter{tkz@gr@a}{#2-1}
     \pgfmathsetcounter{tkz@gr@b}{#2}
     \edef\tkz@auxctp{\thetkz@gr@a}
     \foreach \lg in {0,...,\tkz@auxctp}{%
        \pgfmathsetcounter{tkz@gr@b}{#2-\lg}
        \setcounter{tkz@gr@b}{\thetkz@gr@b}
        \edef\tkzb@rtemp{\cmdGR@cl@RA}
        \edef\tkzb@ptemp{\cmdGR@cl@prefix}
        \pgfmathmultiply{\cmdGR@cl@RA}{\lg}
        \let\myresult\pgfmathresult
        \begin{scope}[xshift=\myresult cm]
           \grPath[#1,%
                   RA     = \tkzb@rtemp,%
                   RS     = \myresult,%
                   prefix = \tkzb@ptemp,%
                   num    = \lg,form=1]{\thetkz@gr@b}%
        \end{scope}%
     }
  \fi%
    \pgfmathsetcounter{tkz@gr@a}{#2-2}
    \edef\tkz@auxctp{\thetkz@gr@a}
    \foreach \V@x in  {0,...,\tkz@auxctp}{%
       \pgfmathsetcounter{tkz@gr@e}{\thetkz@gr@a-\V@x}
       \edef\tkz@auxctpb{\thetkz@gr@e}
       \foreach \V@y in  {0,...,\tkz@auxctpb}{%
          \pgfmathsetcounter{tkz@gr@b}{\V@y+1}
  \Edge(\cmdGR@cl@prefix\V@x\grLabelSep\V@y)%
       (\cmdGR@cl@prefix\V@x\grLabelSep\thetkz@gr@b)
          \pgfmathsetcounter{tkz@gr@p}{\V@x+1}
          \Edge(\cmdGR@cl@prefix\V@x\grLabelSep\thetkz@gr@b)%
               (\cmdGR@cl@prefix\thetkz@gr@p\grLabelSep\V@y)
       }%
    }
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                                 grHeawood
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grHeawood}[1][]{% #1 options #2 ordre du graphe
\begingroup%
  \setkeys[GR]{cl}{#1}%
  \grCycle[#1]{14}
  \EdgeInGraphMod*{\cmdGR@cl@prefix}{14}{5}{0}{2}
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                               grCirculant #1 option #2 vertex #3 add k
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grCirculant}[3][]{%
\begingroup%
    \setkeys[GR]{cl}{#1}
    \grEmptyCycle[#1]{#2}%
    \pgfmathisprime{#2}%
    \ifnum\pgfmathresult=1\relax
       \foreach \kci in {#3}{%
          \EdgeInGraphMod{\cmdGR@cl@prefix}{#2}{\kci}}%
     \else
       \foreach \kci in {#3}{%
          \pgfmathisfactor{#2}{\kci}%
           \ifnum\pgfmathresult=1\relax
             \pgfmathsetcounter{tkz@gr@a}{\kci-1}
             \edef\tkz@auxctp{\thetkz@gr@a}
             \foreach \start in {0,...,\tkz@auxctp}{%
                \setcounter{tkz@gr@i}{\start}%
                \setcounter{tkz@gr@n}{#2}%
                \whiledo{\not\equal{\value{tkz@gr@n}}{\start}}{%
                  \pgfmathsetcounter{tkz@gr@n}{Mod(\thetkz@gr@i+\kci,#2)}
                  \Edge(\cmdGR@cl@prefix\thetkz@gr@i)%
                       (\cmdGR@cl@prefix\thetkz@gr@n)%
                  \pgfmathsetcounter{tkz@gr@i}{\thetkz@gr@n}%
                  }%
               }%
              \else
       \EdgeInGraphMod{\cmdGR@cl@prefix}{#2}{\kci}
       \fi
       }%
       \fi
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                               grPetersenG
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grGeneralizedPetersen}[3][]{%
\begingroup%
   \setkeys[GR]{cl}{#1}%
   \grCycle[#1]{#2}
   \edef\tkzb@rtemp{\cmdGR@cl@RB}
   \edef\tkzb@pptemp{\cmdGR@cl@prefixx}
   \edef\tkzb@ptemp{\cmdGR@cl@prefix}
   \grCirculant[#1,RA=\tkzb@rtemp,prefix=\tkzb@pptemp]{#2}{#3}
   \EdgeIdentity{\tkzb@ptemp}{\cmdGR@cl@prefixx}{#2}
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                               grPetersen
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grStartwo}[2][]{%
\begingroup%
   \setkeys[GR]{cl}{#1}%
   \pgfmathsetcounter{tkz@gr@e}{3*#2-2}
   \pgfmathsetcounter{tkz@gr@a}{3*#2-1}
   \grEmptyCycle[#1]{\thetkz@gr@a}
   \EdgeInGraphMod{\cmdGR@cl@prefix}{\thetkz@gr@a}{#2}%
\endgroup%
}

\newcommand*{\grPetersen}[1][]{%
\begingroup%
    \setkeys[GR]{cl}{#1}%
    \ifcase\cmdGR@cl@form
      \or
        \grCycle[#1]{5}%
        \edef\tkzb@rtemp{\cmdGR@cl@RB}
        \edef\tkzb@ptemp{\cmdGR@cl@prefixx}
        \grStartwo[#1,RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{2}
        \EdgeIdentity{\cmdGR@cl@prefix}{\cmdGR@cl@prefixx}{5}
      \or
         \grCycle[#1]{6}
         \begin{scope}[rotate=30]
            \edef\tkzb@rtemp{\cmdGR@cl@RB}
            \edef\tkzb@ptemp{\cmdGR@cl@prefixx}
            \grStar[#1,RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{4}
          \end{scope}
          \setcounter{tkz@gr@a}{2}
          \foreach \V@x in  {0,...,5}{%
             \ifthenelse{\equal{\thetkz@gr@a}{-1}}{%
                \setcounter{tkz@gr@a}{2}}{%
                }%
                \Edge(\cmdGR@cl@prefix\V@x)(\cmdGR@cl@prefixx\thetkz@gr@a)
                \addtocounter{tkz@gr@a}{-1}%
             }%
     \or
       \grEmptyStar[#1]{10}
       \EdgeInGraphLoop{\cmdGR@cl@prefix}{9}
       \EdgeInGraphMod*{\cmdGR@cl@prefix}{9}{4}{0}{3}
       \foreach \V@x in  {2,5,8}{%
         \Edge(\cmdGR@cl@prefix\V@x)(\cmdGR@cl@prefix 9)}%
     \fi
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                               grPlatonic
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grTetrahedral}[1][]{% 
\begingroup%
  \setkeys[GR]{cl}{#1}%
  \begin{scope}[rotate=90]
    \grWheel[#1]{4}%
  \end{scope}
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                       grOctahedral
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grOctahedral}[1][]{% 
\begingroup%
   \setkeys[GR]{cl}{#1}%
   \grComplete[#1]{3}%
   \begin{scope}[rotate=-60]
          \edef\tkzb@rtemp{\cmdGR@cl@RB}
          \edef\tkzb@ptemp{\cmdGR@cl@prefixx}
          \grComplete[#1,RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{3}%
   \end{scope}
   \EdgeIdentity{\cmdGR@cl@prefix}{\cmdGR@cl@prefixx}{3}
   \EdgeMod{\cmdGR@cl@prefix}{\cmdGR@cl@prefixx}{3}{1}
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                           grCubicalGraph
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grCubicalGraph}[1][]{%
\begingroup%
    \setkeys[GR]{cl}{#1}%
       \grCycle[#1]{4}
       \edef\tkzb@ptemp{\cmdGR@cl@prefixx}
       \edef\tkzb@rtemp{\cmdGR@cl@RB}
       \grCycle[#1,RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{4}
    \ifcase\cmdGR@cl@form
      \or
        \EdgeIdentity{\cmdGR@cl@prefix}{\cmdGR@cl@prefixx}{4}
      \or
        \EdgeMod*{\cmdGR@cl@prefix}{\cmdGR@cl@prefixx}{4}{1}{2}
        \EdgeMod*{\cmdGR@cl@prefixx}{\cmdGR@cl@prefix}{4}{1}{2}
     \fi
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                         grIcosahedral
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grIcosahedral}[1][]{% 
\begingroup%
   \setkeys[GR]{cl}{#1}%
    \ifcase\cmdGR@cl@form
      \or
       \grCycle[#1]{6}%
       \edef\tkzb@rtemp{\cmdGR@cl@RB}
       \edef\tkzb@ptemp{\cmdGR@cl@prefixx}
       \grCirculant[RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{6}{2}
       \EdgeIdentity{\cmdGR@cl@prefix}{\cmdGR@cl@prefixx}{6}
      \EdgeMod{\cmdGR@cl@prefixx}{\cmdGR@cl@prefix}{6}{1}
      \EdgeMod{\cmdGR@cl@prefixx}{\cmdGR@cl@prefix}{6}{-1}
      \or
       \grCycle[#1]{3}
       \edef\tkzb@rtemp{\cmdGR@cl@RB}
       \edef\tkzb@ptemp{\cmdGR@cl@prefixx}
       \grCycle[RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{6}%
       \begin{scope}[rotate=60]
         \edef\tkzb@rtemp{\cmdGR@cl@RC}
         \edef\tkzb@ptemp{\cmdGR@cl@prefixxx}
         \grCycle[RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{3}%
       \end{scope}
       \setcounter{tkz@gr@a}{2}
       \foreach \st in  {5,0,1}{%
         \foreach \v in  {0,1,2}{%
           \pgfmathsetcounter{tkz@gr@n}{Mod((\thetkz@gr@a*\v)+\st,6)}%
           \Edge(\cmdGR@cl@prefix\v)(\cmdGR@cl@prefixx\thetkz@gr@n)
           }%
         }%
       \setcounter{tkz@gr@a}{2}
       \foreach \v in  {0,1,2}{%
         \foreach \st in  {0,1,2}{%
           \pgfmathsetcounter{tkz@gr@n}{Mod(\thetkz@gr@a*\v+\st,6)}%
           \Edge(\cmdGR@cl@prefixxx\v)(\cmdGR@cl@prefixx\thetkz@gr@n)
           }%
        }%
    \fi
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                       grDodecahedral
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grDodecahedral}[1][]{% 
\begingroup%
\setkeys[GR]{cl}{#1}%
   \ifcase\cmdGR@cl@form
     \or
       \grCycle[#1]{10}
        \edef\tkzb@rtemp{\cmdGR@cl@RB}
        \edef\tkzb@ptemp{\cmdGR@cl@prefixx}
        \grCirculant[RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{10}{2}
        \EdgeIdentity{\cmdGR@cl@prefix}{\cmdGR@cl@prefixx}{10}
      \or
       \grCycle[#1]{5}
       \begin{scope}[rotate=36]
          \edef\tkzb@rtemp{\cmdGR@cl@RC}
          \edef\tkzb@ptemp{\cmdGR@cl@prefixxx}
          \grEmptyCycle[RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{5}
       \end{scope}
       \edef\tkzb@rtemp{\cmdGR@cl@RB}
        \edef\tkzb@ptemp{\cmdGR@cl@prefixx}
        \grEmptyCycle[RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{5}
        \begin{scope}[rotate=36]
          \edef\tkzb@rtemp{\cmdGR@cl@RD}
          \edef\tkzb@ptemp{\cmdGR@cl@prefixxxx}
          \grCycle[RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{5}%
        \end{scope}
        \EdgeIdentity{\cmdGR@cl@prefix}{\cmdGR@cl@prefixx}{5}
        \EdgeIdentity{\cmdGR@cl@prefixxx}{\cmdGR@cl@prefixxxx}{5}
        \EdgeIdentity{\cmdGR@cl@prefixx}{\cmdGR@cl@prefixxx}{5}
        \EdgeMod{\cmdGR@cl@prefixx}{\cmdGR@cl@prefixxx}{5}{-1}
     \or
       \grCycle[#1]{5}
       \begin{scope}[rotate=36]
         \edef\tkzb@rtemp{\cmdGR@cl@RC}
         \edef\tkzb@ptemp{\cmdGR@cl@prefixxx}
         \grEmptyCycle[RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{5}
       \end{scope}
       \edef\tkzb@rtemp{\cmdGR@cl@RB}
       \edef\tkzb@ptemp{\cmdGR@cl@prefixx}
       \grCycle[RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{10}
       \EdgeInGraphLoop{\cmdGR@cl@prefixxx}{5}
       \EdgeDoubleMod{\cmdGR@cl@prefix}{5}{0}{1}%
                     {\cmdGR@cl@prefixx}{10}{0}{2}{5}
       \EdgeDoubleMod{\cmdGR@cl@prefixxx}{5}{0}{1}%
                     {\cmdGR@cl@prefixx}{10}{1}{2}{5}
     \or
       \grLCF[#1]{10,7,4,-4,-7,10,-4,7,-7,4}{2}
     \or
        \grCycle[#1]{10}
        \edef\tkzb@rtemp{\cmdGR@cl@RB}
        \edef\tkzb@ptemp{\cmdGR@cl@prefixx}
        \grEmptyCycle[RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{6}
        \begin{scope}[rotate=45]
          \edef\tkzb@rtemp{\cmdGR@cl@RC}
          \edef\tkzb@ptemp{\cmdGR@cl@prefixxx}
          \grEmptyCycle[RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{4}%
        \end{scope}
       \setcounter{tkz@gr@a}{0}
       \foreach \v in  {1,4,6,9}{%
           \Edge(\cmdGR@cl@prefix\v)(\cmdGR@cl@prefixxx\thetkz@gr@a)
           \stepcounter{tkz@gr@a}
           }%
       \setcounter{tkz@gr@a}{0}
       \foreach \v in  {2,1,5,4}{%
           \Edge(\cmdGR@cl@prefixx\v)(\cmdGR@cl@prefixxx\thetkz@gr@a)
           \stepcounter{tkz@gr@a}
           }%
       \setcounter{tkz@gr@a}{0}
       \foreach \v in  {0,2,3,5,7,8}{%
           \Edge(\cmdGR@cl@prefix\v)(\cmdGR@cl@prefixx\thetkz@gr@a)
           \stepcounter{tkz@gr@a}
           }%
       \Edge(\cmdGR@cl@prefixxx0)(\cmdGR@cl@prefixxx3)
       \Edge(\cmdGR@cl@prefixxx1)(\cmdGR@cl@prefixxx2)
       \Edge(\cmdGR@cl@prefixx0)(\cmdGR@cl@prefixx1)
       \Edge(\cmdGR@cl@prefixx0)(\cmdGR@cl@prefixx5)
       \Edge(\cmdGR@cl@prefixx3)(\cmdGR@cl@prefixx2)
       \Edge(\cmdGR@cl@prefixx3)(\cmdGR@cl@prefixx4)
\fi
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                     grMobiusKantor
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grMobiusKantor}[1][]{% #1 options #2 ordre du graphe
\begingroup%
  \setkeys[GR]{cl}{#1}
   \ifcase\cmdGR@cl@form
     \or
       \grCycle[#1]{16}
       \EdgeInGraphMod*{\cmdGR@cl@prefix}{16}{5}{0}{2}
     \or
       \grCycle[#1]{8}
       \edef\tkzb@rtemp{\cmdGR@cl@RB}
       \edef\tkzb@ptemp{\cmdGR@cl@prefixx}
       \grCirculant[RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{8}{3}
       \EdgeIdentity{\cmdGR@cl@prefix}{\cmdGR@cl@prefixx}{8}
     \or
       \grCirculant[#1]{8}{3} 
       \edef\tkzb@rtemp{\cmdGR@cl@RB}
       \edef\tkzb@ptemp{\cmdGR@cl@prefixx}
       \grCycle[#1,RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{8}
       \EdgeIdentity{\cmdGR@cl@prefix}{\cmdGR@cl@prefixx}{8}
     \fi
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                     grMoebiusLadder
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grMobiusLadder}[2][]{%
\begingroup%
  \setkeys[GR]{cl}{#1}
  \grEmptyCycle[#1]{#2}
  \pgfmathsetcounter{tkz@gr@p}{#2-1}
  \edef\tkzb@rtemp{\cmdGR@cl@RB}
  \edef\tkzb@ptemp{\cmdGR@cl@prefixx}
  \grEmptyCycle[RA=\tkzb@rtemp,prefix=\tkzb@ptemp]{#2}%
  \EdgeIdentity{\cmdGR@cl@prefix}{\cmdGR@cl@prefixx}{#2}
  \EdgeInGraphLoop*{\cmdGR@cl@prefix}{#2}
  \EdgeInGraphLoop*{\cmdGR@cl@prefixx}{#2}
  \Edge(\cmdGR@cl@prefix0)(\cmdGR@cl@prefixx\thetkz@gr@p)
  \Edge(\cmdGR@cl@prefixx0)(\cmdGR@cl@prefix\thetkz@gr@p)
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                     grCocktailParty 
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grCocktailParty}[2][]{%
\begingroup%
  \setkeys[GR]{cl}{#1}%
  \pgfmathsetcounter{tkz@gr@p}{#2-1}
  \grPath[#1,RS=0]{#2}
  \edef\tkzb@ptemp{\cmdGR@cl@prefixx}
  \edef\tkzb@rtemp{\cmdGR@cl@RS}
  \grPath[#1,prefix=\tkzb@ptemp,RS=\tkzb@rtemp]{#2}
   \edef\tkz@auxctp{\thetkz@gr@p}
  \foreach \cpx in {0,...,\tkz@auxctp}{%
      \EdgeFromOneToComp{\cmdGR@cl@prefix}{\cmdGR@cl@prefixx}{\cpx}{#2}
      }
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                     grCrown 
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grCrown}[2][]{%
\begingroup%
  \setkeys[GR]{cl}{#1}%
  \pgfmathsetcounter{tkz@gr@p}{#2-1}
  \grEmptyPath[#1,RS=0]{#2}
  \edef\tkzb@ptemp{\cmdGR@cl@prefixx}
  \edef\tkzb@rtemp{\cmdGR@cl@RS}
  \grEmptyPath[#1,prefix=\tkzb@ptemp,RS=\tkzb@rtemp]{#2}
  \edef\tkz@auxctp{\thetkz@gr@p}  
  \foreach \cpx in {0,...,\thetkz@gr@p}{%
      \EdgeFromOneToComp{\cmdGR@cl@prefix}{\cmdGR@cl@prefixx}{\cpx}{#2}
      }
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                     grMcGee 
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grMcGee}[1][]{%
\begingroup%
  \setkeys[GR]{cl}{#1}%
  \grLCF[#1]{-12,7,-7}{8}
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                     grRobertson 
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grRobertson}[1][]{%
\begingroup%
  \setkeys[GR]{cl}{#1}%
  \grLCF[#1]{8,4,7,4,8,5,7,4,7,8,4,5,7,8,4,8,4,8,4}{1}
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                     grRobertsonWegner 
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grRobertsonWegner}[1][]{%
\begingroup%
  \setkeys[GR]{cl}{#1}%
    \grLCF[#1]{6,12}{15}
    \EdgeInGraphMod{\cmdGR@cl@prefix}{30}{9}{1}{6}
    \EdgeInGraphMod*{\cmdGR@cl@prefix}{30}{15}{2}{6}
    \EdgeInGraphMod*{\cmdGR@cl@prefix}{30}{9}{3}{6}
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                     grDoyle 
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grDoyle}[1][]{%
\begingroup%
    \setkeys[GR]{cl}{#1}%
    \ifcase\cmdGR@cl@form
      \or
        \grCycle[#1]{9}
        \begin{scope}[rotate=18]
          \edef\tkzb@ptemp{\cmdGR@cl@prefixx}
          \edef\tkzb@rtemp{\cmdGR@cl@RB}
          \grCirculant[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{9}{2}
        \end{scope}
        \EdgeMod{\cmdGR@cl@prefixx}{\cmdGR@cl@prefix}{9}{1}
        \edef\tkzb@ptemp{\cmdGR@cl@prefixxx}
        \edef\tkzb@rtemp{\cmdGR@cl@RC}
        \grCirculant[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{9}{4}
        \EdgeIdentity{\cmdGR@cl@prefix}{\cmdGR@cl@prefixxx}{9}
        \EdgeMod{\cmdGR@cl@prefixx}{\cmdGR@cl@prefixxx}{9}{1}
      \or
        \grCycle[#1]{27}
        \EdgeDoubleMod{\cmdGR@cl@prefix}{27}{0}{3}
                      {\cmdGR@cl@prefix}{27}{13}{3}{9}
        \EdgeDoubleMod{\cmdGR@cl@prefix}{27}{1}{3}
                      {\cmdGR@cl@prefix}{27}{5}{3}{9}
        \EdgeDoubleMod{\cmdGR@cl@prefix}{27}{0}{3}
                      {\cmdGR@cl@prefix}{27}{20}{3}{9}
      \or
        \grCycle[#1]{27}
        \EdgeDoubleMod{\cmdGR@cl@prefix}{27}{17}{1}
                      {\cmdGR@cl@prefix}{27}{10}{-2}{4}
        \EdgeDoubleMod{\cmdGR@cl@prefix}{27}{26}{1}
                      {\cmdGR@cl@prefix}{27}{19}{-2}{4}
        \EdgeDoubleMod{\cmdGR@cl@prefix}{27}{8}{1}
                      {\cmdGR@cl@prefix}{27}{1}{-2}{4}
        \EdgeDoubleMod{\cmdGR@cl@prefix}{27}{4}{1}
                      {\cmdGR@cl@prefix}{27}{27}{-2}{3}
        \EdgeDoubleMod{\cmdGR@cl@prefix}{27}{8}{1}
                      {\cmdGR@cl@prefix}{27}{1}{-2}{4}
        \EdgeDoubleMod{\cmdGR@cl@prefix}{27}{14}{1}
                      {\cmdGR@cl@prefix}{27}{7}{-2}{2}
        \EdgeDoubleMod{\cmdGR@cl@prefix}{27}{23}{1}
                      {\cmdGR@cl@prefix}{27}{16}{-2}{2}
        \Edge(\cmdGR@cl@prefix9)(\cmdGR@cl@prefix13)%
        \Edge(\cmdGR@cl@prefix18)(\cmdGR@cl@prefix22)%
    \fi
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                     grDesargues 
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grDesargues}[1][]{%
\begingroup%
    \setkeys[GR]{cl}{#1}%
    \ifcase\cmdGR@cl@form
      \or
        \grLCF[#1]{5,-5,9,-9}{5}
      \or
         \grGeneralizedPetersen[#1]{10}{3}
     \fi
\endgroup%
}

%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                     grKonisberg
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% #1 prefix  #2 indice #2 prefix #3 indice choisie entre #4 et #5 ...
\newcommand{\grKonisberg}[1][]{%
\begingroup%
  \setkeys[GR]{cl}{#1}%
   \grCycle[#1]{4}
   \Edge[style={bend left}](\cmdGR@cl@prefix1)(\cmdGR@cl@prefix2)
   \Edge[style={bend left}](\cmdGR@cl@prefix2)(\cmdGR@cl@prefix3) 
   \Edge(\cmdGR@cl@prefix0)(\cmdGR@cl@prefix2)
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                     grWong
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>

\newcommand{\grWong}[1][]{%
\begingroup%
   \setkeys[GR]{cl}{#1}%
    \grLCF[#1]{8,4,12,4,8,4}{5}
    \EdgeInGraphMod*{\cmdGR@cl@prefix}{30}{15}{0}{3}
    \EdgeInGraphMod*{\cmdGR@cl@prefix}{30}{16}{1}{6}
    \EdgeInGraphMod*{\cmdGR@cl@prefix}{30}{18}{4}{6}
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                     grTutte
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>

\newcommand{\grTutteCoxeter}[1][]{%
\begingroup%
   \setkeys[GR]{cl}{#1}%
    \grLCF[#1]{-13,-9,7,-7,9,13}{5}
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                     grFoster
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>

\newcommand{\grFoster}[1][]{%
\begingroup%
   \setkeys[GR]{cl}{#1}%
    \grLCF[#1]{17,-9,37,-37,9,-17}{15}
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                     grFolkman
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>

\newcommand{\grFolkman}[1][]{%
\begingroup%
   \setkeys[GR]{cl}{#1}%
  \grLCF[#1]{5,-7,-7,5}{5}
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                     grFranklin
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>

\newcommand{\grFranklin}[1][]{%
\begingroup%
   \setkeys[GR]{cl}{#1}%
  \grLCF[#1]{5,-5}{6}
\endgroup%
}

%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                     grNauru
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>

\newcommand{\grNauru}[1][]{%
\begingroup%
   \setkeys[GR]{cl}{#1}%
  \grLCF[#1]{5, −9, 7, −7, 9, −5}{4}
\endgroup%
} 

%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                     grDick
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>

\newcommand{\grDick}[1][]{%
\begingroup%
   \setkeys[GR]{cl}{#1}%
  \grLCF[#1]{5,-5,13,-13}{8}
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                     grHarries
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>

\newcommand{\grHarries}[1][]{%
\begingroup%
   \setkeys[GR]{cl}{#1}%
  \grLCF[#1]{-29,-19,-13,13,21,-27,27,33,-13,13,19,-21,-33,29}{5}
\endgroup%
}   
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                     grAndrasfai
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcounter{tkza@tmp}  
 \newcommand*{\grAndrasfai}[2][]{%
 \begingroup
    \setkeys[GR]{cl}{#1}%
    \pgfmathsetcounter{tkz@bg@cnt}{3*#2-1}
     \grEmptyCycle[#1]{\thetkz@bg@cnt}
   \pgfmathsetcounter{tkza@tmp}{\thetkz@bg@cnt/2}
   \pgfmathsetcounter{tkza@tmp}{\thetkz@bg@cnt+1}
   \pgfmathsetcounter{tkz@gr@p}{1}  
   \whiledo{\value{tkz@gr@p} < \value{tkza@tmp}}{%
      \EdgeInGraphMod*{\cmdGR@cl@prefix}{\thetkz@bg@cnt}{\thetkz@gr@p}{0}{1}
      \pgfmathsetcounter{tkz@gr@p}{\thetkz@gr@p+3}
      }   
\endgroup
}  
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                                 grGrotzsch
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grGrotzsch}[1][]{%
\begingroup%
    \setkeys[GR]{cl}{#1}%
    \ifcase\cmdGR@cl@form
      \or
     \begin{scope}[rotate=18]%
       \grStar[#1]{6}%
          \edef\tkzb@ptemp{\cmdGR@cl@prefixx}
          \edef\tkzb@rtemp{\cmdGR@cl@RB}
       \grCycle[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{5}%
       \Edges(\cmdGR@cl@prefix0,\cmdGR@cl@prefixx1,%
              \cmdGR@cl@prefix2,\cmdGR@cl@prefixx3,%
              \cmdGR@cl@prefix4,\cmdGR@cl@prefixx0,%
              \cmdGR@cl@prefix1,\cmdGR@cl@prefixx2,%
              \cmdGR@cl@prefix3,\cmdGR@cl@prefixx4,\cmdGR@cl@prefix0)
     \end{scope}
      \or
     \begin{scope}[rotate=18]%
       \grStar[#1]{6}%
          \edef\tkzb@ptemp{\cmdGR@cl@prefixx}
          \edef\tkzb@rtemp{\cmdGR@cl@RB}
       \begin{scope}[rotate=-36]%
          \grCirculant[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{5}{2}%
       \end{scope}
     \EdgeDoubleMod{a}{5}{0}{1}%
                   {b}{5}{1}{1}{4}
     \EdgeIdentity{a}{b}{5}
     \end{scope}
\fi
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                                 grLevi
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grLevi}[1][]{%
\begingroup%
    \setkeys[GR]{cl}{#1}%
    \ifcase\cmdGR@cl@form
      \or
         \grLCF[#1]{-13,-9,7,-7,9,13}{5}
      \or
    \grCycle[#1]{10}
    \EdgeInGraphMod{\cmdGR@cl@prefix}{10}{5}
    \edef\tkzb@ptemp{\cmdGR@cl@prefixx}
    \edef\tkzb@rtemp{\cmdGR@cl@RB}
    \grEmptyCycle[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{10}
    \edef\tkzb@ptemp{\cmdGR@cl@prefixxx}
    \edef\tkzb@rtemp{\cmdGR@cl@RC}
    \grEmptyCycle[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{10}
    \EdgeInGraphMod{\cmdGR@cl@prefixxx}{10}{4}
\fi
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                                 grPappus
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grPappus}[1][]{%
\begingroup%
    \setkeys[GR]{cl}{#1}%
    \ifcase\cmdGR@cl@form
\or
    \grLCF[#1]{5,7,-7,7,-7,-5}{3}
\or
 \begin{scope}[rotate=30]%
   \grCycle[#1]{6}
          \edef\tkzb@ptemp{\cmdGR@cl@prefixx}
          \edef\tkzb@rtemp{\cmdGR@cl@RB}
   \grCycle[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{6}
          \edef\tkzb@ptemp{\cmdGR@cl@prefixxx}
          \edef\tkzb@rtemp{\cmdGR@cl@RC}
   \grCycle[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{6}
   \EdgeDoubleMod{\cmdGR@cl@prefixxx}{6}{0}{2}%
                 {\cmdGR@cl@prefixx}{6}{5}{2}{2}
   \EdgeDoubleMod{\cmdGR@cl@prefixxx}{6}{5}{2}%
                 {\cmdGR@cl@prefix}{6}{1}{2}{2}
   \EdgeDoubleMod{\cmdGR@cl@prefixx}{6}{0}{2}%
                 {\cmdGR@cl@prefix}{6}{0}{2}{2}
\end{scope}
\or
 \begin{scope}[rotate=30]
   \grCycle[#1]{6}
          \edef\tkzb@ptemp{\cmdGR@cl@prefixx}
          \edef\tkzb@rtemp{\cmdGR@cl@RB}
   \grCirculant[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{6}{2}
          \edef\tkzb@ptemp{\cmdGR@cl@prefixxx}
          \edef\tkzb@rtemp{\cmdGR@cl@RC}
   \grEmptyCycle[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{6}
   \EdgeIdentity{\cmdGR@cl@prefixx}{\cmdGR@cl@prefix}{6}
   \EdgeInGraphMod{\cmdGR@cl@prefixxx}{6}{3}   
\end{scope} 
\fi
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                                 grChvatal
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grChvatal}[1][]{%
\begingroup%
\setkeys[GR]{cl}{#1}%
\ifcase\cmdGR@cl@form
\or
  \begin{scope}[rotate=45]
    \grCycle[#1]{4}
    \end{scope}
    \edef\tkzb@ptemp{\cmdGR@cl@prefixx}
    \edef\tkzb@rtemp{\cmdGR@cl@RB}
  \begin{scope}[rotate=22.25]
    \grEmptyCycle[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{8}
  \end{scope}
  \EdgeInGraphMod{\cmdGR@cl@prefixx}{8}{4}
  \EdgeInGraphMod*{\cmdGR@cl@prefixx}{8}{1}{1}{2}
  \EdgeInGraphMod*{\cmdGR@cl@prefixx}{8}{3}{1}{2}
   \EdgeDoubleMod{\cmdGR@cl@prefix}{4}{0}{1}%
                 {\cmdGR@cl@prefixx}{8}{1}{2}{3}
   \EdgeDoubleMod{\cmdGR@cl@prefix}{4}{0}{1}%
                 {\cmdGR@cl@prefixx}{8}{0}{2}{3} 
\or
   \begin{scope}[rotate=18]
     \grCycle[#1]{5}
     \edef\tkzb@ptemp{\cmdGR@cl@prefixx}
     \edef\tkzb@rtemp{\cmdGR@cl@RB}
     \grEmptyCycle[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{5}
   \end{scope} 
   \edef\tkzb@ptemp{\cmdGR@cl@prefixxx}
   \edef\tkzb@rtemp{\cmdGR@cl@RC} 
   \grEmptyCycle[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{2}
   \EdgeDoubleMod{\cmdGR@cl@prefix}{5}{0}{1}%
                 {\cmdGR@cl@prefixx}{5}{1}{1}{4}
   \EdgeDoubleMod{\cmdGR@cl@prefix}{5}{0}{1}%
                 {\cmdGR@cl@prefixx}{5}{4}{1}{4}
   \EdgeFromOneToSel{\cmdGR@cl@prefixxx}{\cmdGR@cl@prefixx}{0}{4,0,1}
   \EdgeFromOneToSel{\cmdGR@cl@prefixxx}{\cmdGR@cl@prefixx}{1}{1,2,3}
   \Edge(\cmdGR@cl@prefixx3)(\cmdGR@cl@prefixx4)
   \Edge(\cmdGR@cl@prefixx0)(\cmdGR@cl@prefixxx1)
   \Edge(\cmdGR@cl@prefixx2)(\cmdGR@cl@prefixxx0)
\or
  \grCycle[#1]{12}
  \Edges(\cmdGR@cl@prefix0,\cmdGR@cl@prefix6,\cmdGR@cl@prefix3,%
         \cmdGR@cl@prefix8,\cmdGR@cl@prefix11,\cmdGR@cl@prefix5,%
         \cmdGR@cl@prefix2,\cmdGR@cl@prefix9,\cmdGR@cl@prefix0)
  \Edges(\cmdGR@cl@prefix1,\cmdGR@cl@prefix7,\cmdGR@cl@prefix10,%
         \cmdGR@cl@prefix4,\cmdGR@cl@prefix1)  
\fi  
\endgroup%
}

%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                                 grBalaban
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\grBalaban}[1][]{%
\begingroup%
\setkeys[GR]{cl}{#1}%
\ifcase\cmdGR@cl@form
\or
     \grCycle[#1]{50}
     \EdgeInGraphMod*{\cmdGR@cl@prefix}{50}{9}{3}{5}
     \EdgeInGraphMod*{\cmdGR@cl@prefix}{50}{25}{0}{5}
     \begin{scope}[rotate=12]
        \edef\tkzb@ptemp{\cmdGR@cl@prefixx}
        \edef\tkzb@rtemp{\cmdGR@cl@RB}
        \grCirculant[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{10}{3}
     \end{scope}
     \begin{scope}[rotate=24]
        \edef\tkzb@ptemp{\cmdGR@cl@prefixxx}
        \edef\tkzb@rtemp{\cmdGR@cl@RC}
       \grCirculant[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{10}{3}
     \end{scope}
     \EdgeDoubleMod{\cmdGR@cl@prefix}{50}{1}{5}%
                   {\cmdGR@cl@prefixx}{10}{0}{1}{10}
     \EdgeDoubleMod{\cmdGR@cl@prefix}{50}{4}{5}%
                   {\cmdGR@cl@prefixxx}{10}{0}{1}{10}
\or
 \begin{scope}[rotate=9]
   \grCycle[#1]{10}
 \end{scope}
 \begin{scope}[rotate=-9]
        \edef\tkzb@ptemp{\cmdGR@cl@prefixx}
        \edef\tkzb@rtemp{\cmdGR@cl@RB}
   \grCycle[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{10}
 \end{scope}
 \begin{scope}[rotate=6]
        \edef\tkzb@ptemp{\cmdGR@cl@prefixxx}
        \edef\tkzb@rtemp{\cmdGR@cl@RC}
   \grEmptyCycle[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{30}
   \EdgeInGraphMod*{\cmdGR@cl@prefixxx}{30}{1}{0}{3}
   \EdgeInGraphMod*{\cmdGR@cl@prefixxx}{30}{1}{1}{3}
   \EdgeInGraphMod*{\cmdGR@cl@prefixxx}{30}{15}{1}{3}
 \end{scope}
 \begin{scope}[rotate=9]
        \edef\tkzb@ptemp{\cmdGR@cl@prefixxxx}
        \edef\tkzb@rtemp{\cmdGR@cl@RD}
   \grEmptyCycle[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{20}
   \EdgeInGraphMod*{\cmdGR@cl@prefixxxx}{20}{7}{0}{2}
   \EdgeInGraphMod*{\cmdGR@cl@prefixxxx}{20}{5}{1}{2}
 \end{scope}
 \EdgeDoubleMod{\cmdGR@cl@prefix}{10}{0}{1}
               {\cmdGR@cl@prefixxx}{30}{0}{3}{9}
 \EdgeDoubleMod{\cmdGR@cl@prefixx}{10}{0}{1}%
               {\cmdGR@cl@prefixxx}{30}{29}{3}{9}
 \EdgeDoubleMod{\cmdGR@cl@prefixxx}{30}{0}{3}%
               {\cmdGR@cl@prefixxxx}{20}{0}{2}{9}
 \EdgeDoubleMod{\cmdGR@cl@prefixxx}{30}{2}{3}%
               {\cmdGR@cl@prefixxxx}{20}{1}{2}{9}
\or
\grEmptyCycle[#1]{10}
\begin{scope}[rotate=9]
      \edef\tkzb@ptemp{\cmdGR@cl@prefixx}
      \edef\tkzb@rtemp{\cmdGR@cl@RB}
  \grEmptyCycle[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{20}
\end{scope}
\begin{scope}[rotate=13]
        \edef\tkzb@ptemp{\cmdGR@cl@prefixxx}
      \edef\tkzb@rtemp{\cmdGR@cl@RC}
  \grEmptyCycle[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{10}
\end{scope}
\begin{scope}[rotate=-13]
        \edef\tkzb@ptemp{\cmdGR@cl@prefixxxx}
      \edef\tkzb@rtemp{\cmdGR@cl@RD}
  \grEmptyCycle[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{10}
\end{scope}
\begin{scope}[rotate=9]
        \edef\tkzb@ptemp{\cmdGR@cl@prefixxxxx}
      \edef\tkzb@rtemp{\cmdGR@cl@RE}
  \grCirculant[#1,prefix=\tkzb@ptemp,RA=\tkzb@rtemp]{20}{6}
\end{scope}
   \EdgeIdentity{\cmdGR@cl@prefixx}{\cmdGR@cl@prefixxxxx}{20}
   \EdgeDoubleMod{\cmdGR@cl@prefix}{10}{0}{1}%
                 {\cmdGR@cl@prefixx}{20}{0}{2}{10}
   \EdgeDoubleMod{\cmdGR@cl@prefix}{10}{0}{1}%
                 {\cmdGR@cl@prefixx}{20}{19}{2}{10}
   \EdgeInGraphMod{\cmdGR@cl@prefix}{10}{5}
   \EdgeDoubleMod{\cmdGR@cl@prefixxx}{10}{0}{1}%
                 {\cmdGR@cl@prefixx}{20}{0}{2}{10}
   \EdgeDoubleMod{\cmdGR@cl@prefixxxx}{10}{0}{1}%
                 {\cmdGR@cl@prefixx}{20}{19}{2}{10}
   \EdgeDoubleMod{\cmdGR@cl@prefixxxx}{10}{0}{1}%
                 {\cmdGR@cl@prefixxx}{10}{1}{1}{10}
   \EdgeDoubleMod{\cmdGR@cl@prefixxxx}{10}{1}{1}%
                 {\cmdGR@cl@prefixxx}{10}{0}{1}{10}
\fi
\endgroup%
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                     Labels
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>

% #2 label/prefix/num
\define@cmdkey [GR] {WL} {color}[black]{}
\define@cmdkey [GR] {WL} {labelstyle}{}
\define@cmdkey [GR] {WL} {size}{}
\define@cmdkey [GR] {WL} {style}{}
\presetkeys    [GR] {WL} {color       = black,%
                          labelstyle  = {},%
                          size        = {},%
                          style       = {}}{}
\newcommand{\grWriteExplicitLabels}[2][]{%
\begingroup%
  \setkeys[GR]{WL}{#1}%
  \foreach \text/\where in {#2}{%
      \node at (\where) {\text};
      }%
\endgroup%
}
\newcommand{\grWriteExplicitLabel}[2][]{%
\begingroup%
  \setkeys[GR]{cl}{#1}%
  \node at (\where) {\text};
\endgroup%
}%
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                               AssignVertexLabel
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\tikzset{AssignStyle/.style={}}
\define@cmdkey [GR] {AVL} {color}{}
\define@cmdkey [GR] {AVL} {size}{}
\define@cmdkey [GR] {AVL} {mathsize}{}
\define@boolkey[GR] {AVL} {Math}[true]{}
\presetkeys    [GR] {AVL} {size       = \normalsize,%
                           mathsize   = \displaystyle,%
                           color      = black,%
                           Math       = false}{} \newcommand*{\AssignVertexLabel}[3][]{%
\begingroup%
  \setkeys[GR]{AVL}{#1}
  \foreach \name [count=\xi from 0] in {#3}{%
  \ifGR@AVL@Math%
     \node at (#2\xi)
       {$\textcolor{\cmdGR@AVL@color}{\cmdGR@AVL@mathsize\name}$};
  \else
   \node[AssignStyle] at (#2\xi)
       {\textcolor{\cmdGR@AVL@color}{\cmdGR@AVL@size\name}};
  \fi}

\endgroup%
}

%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                     grEdgeForTree
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% #1 prefix  #2 indice #2 prefix #3 indice choisie entre #4 et #5 ...
\newcommand{\grEdgeForTree}[5]{%
\begingroup%
  \foreach \V@x in {#4,...,#5}{%
      \Edge(#1#2)(#3\V@x)%
      }%
\endgroup%
}

\newcommand{\grSubtreeOfCage}[3][]{%
  \begingroup
  \setkeys[GR]{cl}{#1}%
  \edef\tkzb@rtemp{\cmdGR@cl@RA}
  \edef\tkzb@rtempx{\cmdGR@cl@RB}
  \edef\tkzb@ptemp{\cmdGR@cl@prefix}
  \ifthenelse{\isodd{#3}}%
  % odd girth
  {%
    \pgfmathsetcounter{tkz@gr@a}{(#3-3)/2}
    \Vertex{\cmdGR@cl@prefix 0\grLabelSep 0}
    \edef\tkz@auxctp{\thetkz@gr@a}
    \foreach \V@x in {0,...,\tkz@auxctp}{%
      \pgfmathsetcounter{tkz@gr@b}{#2*((#2-1)^\V@x)}%
      \pgfmathsetmacro{\sep@path}{\tkzb@rtemp/((#2-1)^\V@x)}%
      \pgfmathsetmacro{\y@h}{\tkzb@rtempx*(\V@x+1)}%
      \pgfmathsetcounter{tkz@gr@c}{\V@x+1}%
      \grEmptyPath[%
      prefix=\tkzb@ptemp\thetkz@gr@c\grLabelSep,
      form=2,
      RA=\sep@path,
      x=0,
      y=\y@h]{\thetkz@gr@b}%
    }%
    % edges from the root of the tree
    \EdgeFromOneToAll{\tkzb@ptemp0\grLabelSep}%
    {\tkzb@ptemp1\grLabelSep}{0}{#2}
    % ca = levels from where extra edges emerge
    % cb = edges per vertex
    \pgfmathsetcounter{tkz@gr@a}{\thetkz@gr@a-1}
\edef\tkz@auxctpa{\thetkz@gr@a}
    \foreach \V@y in {0,...,\tkz@auxctpa}{%
      \pgfmathsetcounter{tkz@gr@b}{#2*(#2-1)^\V@y-1}
\edef\tkz@auxctpb{\thetkz@gr@b}
    \foreach \a in {0,...,\tkz@auxctpb}{%
       \pgfmathsetcounter{tkz@gr@c}{\a*(#2-1)}%
       \pgfmathsetcounter{tkz@gr@d}{\a*(#2-1)+(#2-2)}%
       \pgfmathsetcounter{tkz@gr@ta}{\V@y+1}
       \pgfmathsetcounter{tkz@gr@tb}{\V@y+2}
       \EdgeFromOneToSeq{\tkzb@ptemp\thetkz@gr@ta\grLabelSep}%
       {\tkzb@ptemp\thetkz@gr@tb\grLabelSep}{\a}%
       {\thetkz@gr@c}{\thetkz@gr@d}
     }%
   }%
 }%
  % even girth
 {%
   \pgfmathsetcounter{tkz@gr@a}{(#3-2)/2}
   \foreach \V@x in {0,...,\thetkz@gr@a}{%
      \pgfmathsetcounter{tkz@gr@b}{2*((#2-1)^\V@x)}%
      \pgfmathsetmacro{\sep@path}{\tkzb@rtemp/((#2-1)^\V@x)}%
      \pgfmathsetmacro{\y@h}{\tkzb@rtempx*\V@x}%
      \pgfmathsetcounter{tkz@gr@c}{\V@x}%
      \grEmptyPath[%
      prefix=\tkzb@ptemp\thetkz@gr@c\grLabelSep,
      form=2,
      RA=\sep@path,
      x=0,
      y=\y@h]{\thetkz@gr@b}%
    }%
    %%%%%
    \Edge%
    (\tkzb@ptemp0\grLabelSep0)%
    (\tkzb@ptemp0\grLabelSep1)
    %%%%
    \pgfmathsetcounter{tkz@gr@a}{\thetkz@gr@a-1}
    \foreach \V@y in {0,...,\thetkz@gr@a}{%
      \pgfmathsetcounter{tkz@gr@b}{2*(#2-1)^\V@y-1}
    \foreach \a in {0,...,\thetkz@gr@b}{%
      \pgfmathsetcounter{tkz@gr@c}{\a*(#2-1)}%
      \pgfmathsetcounter{tkz@gr@d}{\a*(#2-1)+(#2-2)}%
      \pgfmathsetcounter{tkz@gr@ta}{\V@y}
      \pgfmathsetcounter{tkz@gr@tb}{\V@y+1}
      \EdgeFromOneToSeq{\tkzb@ptemp\thetkz@gr@ta\grLabelSep}%
      {\tkzb@ptemp\thetkz@gr@tb\grLabelSep}{\a}%
      {\thetkz@gr@c}{\thetkz@gr@d}
      }%
    }%
  }%
  \endgroup
}

%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                                  The End
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\catcode`\@=\tkzAtCode\relax  
\endinput