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authorNorbert Preining <norbert@preining.info>2020-03-10 03:01:27 +0000
committerNorbert Preining <norbert@preining.info>2020-03-10 03:01:27 +0000
commit877268a0de707a979be934d888518f6cc02d73a6 (patch)
tree30597445c86d75b20a836b6c90ab6c31b76d902e /macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Folkman.tex
parent0561778af6f8fde0a3a1c334e2aab9a4f1142d6e (diff)
CTAN sync 202003100301
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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