\newpage\section{Doyle}\label{doyle} %<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> %<––––––––––––––––––––––––––––– Doyle ––––––––––––––––––––––––––––––––> %<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> \begin{NewMacroBox}{grDoyle}{\oarg{options}} \medskip From MathWord : \url{http://mathworld.wolfram.com/DoyleGraph.html} \emph{The Doyle graph, sometimes also known as the Holt graph (Marušič et al. 2005), is the symmetric quartic graph on 27 nodes illustrated. It is a Symmetric Graph. Three embeddings are illustrated below.} \href{http://mathworld.wolfram.com/topics/GraphTheory.html}% {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}% {\textcolor{blue}{E.Weisstein}} \medskip The Doyle graph is implemented in \tkzname{tkz-berge} as \tkzcname{grDoyle} with three forms. \end{NewMacroBox} \subsection{\tkzname{The Doyle graph : form 1}} \begin{center} \begin{tkzexample}[vbox] \begin{tikzpicture}[scale=.6] \GraphInit[vstyle=Shade] \SetGraphShadeColor{red}{Maroon}{fondpaille} \SetVertexNoLabel \grDoyle[RA=7,RB=5,RC=3] \end{tikzpicture} \end{tkzexample} \end{center} \vfill\newpage \subsection{\tkzname{The Doyle graph : form 2}} \begin{center} \begin{tkzexample}[vbox] \begin{tikzpicture} \GraphInit[vstyle=Shade] \SetGraphShadeColor{red}{Magenta}{white} \SetVertexNoLabel \grDoyle[form=2,RA=7] \end{tikzpicture} \end{tkzexample} \end{center} \vfill\newpage \subsection{\tkzname{The Doyle graph : form 3}} \begin{center} \begin{tkzexample}[vbox] \begin{tikzpicture} \SetGraphArtColor{red}{Magenta}{red} \GraphInit[vstyle=Shade] \SetVertexNoLabel \grDoyle[form=3,RA=7,RB=2] \end{tikzpicture} \end{tkzexample} \end{center} \vfill\newpage \subsection{27 nodes but not isomorphic to the Doyle graph} \begin{center} \begin{tkzexample}[vbox] \begin{tikzpicture}[scale=.6] \tikzstyle{VertexStyle} = [shape = circle, ball color = gray!60, minimum size = 16pt,draw] \tikzstyle{EdgeStyle} = [thick,color=black,% double = orange,% double distance = 1pt] \SetVertexNoLabel \grCycle[RA=7.5]{9} \grEmptyCycle[prefix=b,RA=5.5]{9} \grCirculant[prefix=c,RA=3.5]{9}{4} \EdgeIdentity{b}{c}{9} \EdgeMod{a}{c}{9}{1} \EdgeMod{a}{b}{9}{1} \EdgeInGraphMod{b}{9}{2} \end{tikzpicture} \end{tkzexample} \end{center} \endinput