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authorNorbert Preining <norbert@preining.info>2021-01-22 03:00:46 +0000
committerNorbert Preining <norbert@preining.info>2021-01-22 03:00:46 +0000
commite1a7798f45cd37c0aa0bfaaef5f0acb4e48bc867 (patch)
treed2bbebcdb7bcb8fe013a9d3cbd2cff880b18afbf /macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Folkman.tex
parent37cb9bbabbfe1a8d0d1334832814ccbefcf9ac0a (diff)
CTAN sync 202101220300
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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 \ No newline at end of file