\newpage\section{Folkman}\label{folkman} %<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> %<–––––––––––––––––––– Folkman –––––––––––––––––––––––––––––––> %<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> \begin{NewMacroBox}{grFolkman}{\oarg{options}} \medskip From MathWorld : \url{http://mathworld.wolfram.com/FolkmanGraph.html} \emph{The Folkman graph is a semisymmetric graph that has the minimum possible number of nodes 20.} \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}} \end{NewMacroBox} \subsection{\tkzname{Folkman Graph LCF embedding}} The code is \begin{tkzexample}[code only] \grLCF[RA=7]{5,-7,-7,5}{5}\end{tkzexample} \begin{center} \begin{tkzexample}[vbox] \begin{tikzpicture}[scale=.8] \GraphInit[vstyle=Art] \SetGraphArtColor{blue}{darkgray} \grFolkman[RA=6] \end{tikzpicture} \end{tkzexample} \end{center} \vfill\newpage \subsection{\tkzname{Folkman Graph embedding 1}} \begin{center} \begin{tkzexample}[vbox] \begin{tikzpicture}[rotate=45]% \tikzstyle{VertexStyle} = [shape = circle, shading = ball, ball color = gray!60, inner sep = 3pt, draw] \tikzstyle{EdgeStyle} = [thick,orange] \SetVertexNoLabel \grCycle[prefix=a,RA=3]{4}% \grCycle[prefix=b,RA=4]{4}% \grCycle[prefix=c,RA=5]{4}% \grCycle[prefix=d,RA=6]{4}% \grCycle[prefix=e,RA=7]{4}% \foreach \r/\s/\t in {a/d/e,b/e/a,c/a/b,d/b/c,e/c/d}{% \Edges(\r0,\s1,\r2,\t3,\r0) } \end{tikzpicture} \end{tkzexample} \end{center} \vfill\newpage \subsection{\tkzname{Folkman Graph embedding 1 new code}} { \tikzstyle{VertexStyle} =[shape = circle,% shading = ball,% inner sep = 4pt,% draw] \tikzstyle{EdgeStyle} = [thin,blue] \begin{center} \begin{tkzexample}[vbox] \begin{tikzpicture} \begin{scope}[shift={(1,1)},rotate=45]\grEmptyPath[prefix=a,RA=1]{5} \end{scope} \begin{scope}[shift={(-1,1)},rotate=135]\grEmptyPath[prefix=b,RA=1]{5} \end{scope} \begin{scope}[shift={(-1,-1)},rotate=225]\grEmptyPath[prefix=c,RA=1]{5} \end{scope} \begin{scope}[shift={(1,-1)},rotate=315]\grEmptyPath[prefix=d,RA=1]{5} \end{scope} \EdgeIdentity*{a}{b}{0,...,4} \EdgeIdentity*{b}{c}{0,...,4} \EdgeIdentity*{c}{d}{0,...,4} \EdgeIdentity*{d}{a}{0,...,4} \EdgeDoubleMod{a}{5}{0}{1}{b}{5}{3}{1}{1} \EdgeDoubleMod{a}{5}{2}{1}{b}{5}{0}{1}{2} \EdgeDoubleMod{a}{5}{1}{1}{d}{5}{0}{1}{3} \EdgeDoubleMod{c}{5}{2}{1}{b}{5}{0}{1}{2} \EdgeDoubleMod{c}{5}{0}{1}{b}{5}{3}{1}{1} \EdgeDoubleMod{c}{5}{1}{1}{d}{5}{0}{1}{3} \Edges(a0,d4,c0) \end{tikzpicture} \end{tkzexample} \end{center} } \vfill\newpage \subsection{\tkzname{Folkman Graph embedding 3}} \begin{center} \begin{tkzexample}[vbox] \begin{tikzpicture}[scale=.8] \SetVertexNoLabel \tikzstyle{VertexStyle} = [shape = circle, shading = ball, ball color = gray!60, inner sep = 3pt, draw] \tikzstyle{EdgeStyle} = [thick,orange] \grEmptyCycle[prefix=a,RA=1.85]{5} \grEmptyCycle[prefix=b,RA=3.7]{5} \grCycle[prefix=c,RA=6]{10} \EdgeDoubleMod{a}{5}{0}{1}{b}{5}{1}{1}{4} \EdgeDoubleMod{a}{5}{0}{1}{b}{5}{4}{1}{4} \EdgeDoubleMod{b}{5}{0}{1}{c}{10}{9}{2}{4} \EdgeDoubleMod{b}{5}{0}{1}{c}{10}{1}{2}{4} \EdgeDoubleMod{a}{5}{0}{1}{c}{10}{8}{2}{4} \EdgeDoubleMod{a}{5}{0}{1}{c}{10}{2}{2}{4} \end{tikzpicture} \end{tkzexample} \end{center} \endinput