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\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
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