\newpage\section{Coxeter} %<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> %<––––––––––––––––––––––––––––– Coxeter ––––––––––––––––––––––––––––––––> %<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> From MathWorld : \url{http://mathworld.wolfram.com/CoxeterGraph.html} The Coxeter graph is a nonhamiltonian cubic symmetric graph on 28 vertices and 42 edges. \subsection{\tkzname{Coxeter graph I}} \bigskip \begin{center} \begin{tkzexample}[vbox] \begin{tikzpicture}[rotate=90,scale=1] \GraphInit[vstyle=Art] \SetGraphArtColor{magenta}{gray} \grCycle[RA=5,prefix=a]{7} \begin{scope}[rotate=-20]\grEmptyCycle[RA=4,prefix=b]{7}\end{scope} \grCirculant[RA=3,prefix=c]{7}{2} \grCirculant[RA=1.4,prefix=d]{7}{3} \EdgeIdentity{a}{b}{7} \EdgeIdentity{b}{c}{7} \EdgeIdentity{b}{d}{7} \end{tikzpicture} \end{tkzexample} \end{center} \vfill\newpage \subsection{\tkzname{Coxeter graph II}} \bigskip \begin{center} \begin{tkzexample}[vbox] \begin{tikzpicture} \GraphInit[vstyle=Art] \SetGraphArtColor{magenta}{gray} \grCycle[RA=7,prefix=b]{24} \grEmptyStar[RA=3,prefix=a]{4} \EdgeDoubleMod{a}{3}{0}{1}{b}{24}{0}{8}{2} \EdgeDoubleMod{a}{3}{0}{1}{b}{24}{7}{8}{2} \EdgeDoubleMod{a}{3}{0}{1}{b}{24}{18}{8}{2} \EdgeDoubleMod{a}{4}{3}{0}{b}{24}{22}{8}{2} \EdgeInGraphMod*{b}{24}{6}{5}{8} \EdgeInGraphMod*{b}{24}{11}{1}{8} \end{tikzpicture} \end{tkzexample} \end{center} \vfill\newpage \subsection{\tkzname{Coxeter graph III}} \bigskip \begin{center} \begin{tkzexample}[vbox] \begin{tikzpicture} \GraphInit[vstyle=Art] \SetGraphArtColor{magenta}{gray} \grCycle[RA=7,prefix=c]{7} \grEmptyCycle[RA=6,prefix=b]{7} \begin{scope}[rotate=12.85]\grEmptyCycle[RA=5,prefix=a]{14}\end{scope} \EdgeIdentity{b}{c}{7} \EdgeDoubleMod{b}{7}{0}{1}{a}{14}{0}{2}{6} \EdgeDoubleMod{b}{7}{0}{1}{a}{14}{13}{2}{6} \EdgeInGraphModLoop{a}{14}{4}{0}{0} \EdgeInGraphModLoop{a}{14}{6}{1}{1} \end{tikzpicture} \end{tkzexample} \end{center} %<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> %<–––––––––––––––––––– Tutte-Coxeter graph ––––––––––––––––––––––––––––> %<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> \vfill\newpage \subsection{\tkzname{Tutte-Coxeter graph I}} \tikzstyle{VertexStyle} = [very thin,draw, shape = circle, color = white, fill = black, inner sep = 0pt, minimum size = 18pt] \tikzstyle{EdgeStyle} = [thick, double = brown, double distance = 1pt] \bigskip \begin{center} \begin{tkzexample}[vbox] \begin{tikzpicture}[scale=3] \GraphInit[vstyle=Art] \SetGraphArtColor{blue}{cyan} \begin{scope}[rotate=5]\grCycle[RA=2.5,prefix=a]{10}\end{scope} \begin{scope}[rotate=-10]\grCirculant[RA=1.8,prefix=b]{10}{5}\end{scope} \begin{scope}[rotate=36]\grCirculant[RA=1.1,prefix=c]{10}{3}\end{scope} \EdgeIdentity{a}{b}{10} \EdgeIdentity{b}{c}{10} \end{tikzpicture} \end{tkzexample} \end{center} % \vfill\newpage \subsection{\tkzname{Tutte-Coxeter graph II}} \bigskip \begin{center} \begin{tkzexample}[vbox] \begin{tikzpicture} \GraphInit[vstyle=Art] \SetGraphArtColor{blue}{darkgray} \grLCF[RA=7]{-13,-9,7,-7,9,13}{5} \end{tikzpicture} \end{tkzexample} \end{center} \endinput