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-\newpage\section{Robertson}\label{robertson}
-%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
-%<–––––––––––––––––––– Robertson –––––––––––––––––––––––––––––––>
-%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
-\begin{NewMacroBox}{grRobertson}{\oarg{options}\var{$k$}}
-
-\medskip
-From MathWord : \url{http://mathworld.wolfram.com/RobertsonGraph.html}
-
-\medskip
-\emph{The Robertson graph is the unique (4,5)-cage graph, illustrated below. It has 19 vertices and 38 edges. It has girth 5, diameter 3, chromatic number 3, and is a quartic graph.}
-\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{Robertson graph with \tkzcname{grRobertson} }}
-
-The cage
-
-\medskip
-\begin{center}
-\begin{tkzexample}[vbox]
-\begin{tikzpicture}[scale=.6]
- \GraphInit[vstyle=Art]
- \SetGraphArtColor{black}{gray}
- \grRobertson[RA=7]
- \end{tikzpicture}
-\end{tkzexample}
-\end{center}
-
-\clearpage\newpage
-\subsection{\tkzname{Fine embedding of the Robertson graph from RV}}
-
-\begin{center}
- \begin{tikzpicture}[scale=.8]
- \tikzstyle{TempEdgeStyle}= [thick,black,%
- double = gray,%
- double distance = 1.5pt]%
- \SetVertexNoLabel
- \renewcommand*{\VertexBigMinSize}{10pt}
- \GraphInit[vstyle=Shade]
- \SetVertexNoLabel
- \SetUpEdge[style = {thick,%
- double = orange,%
- double distance = 1pt}]
- \SetGraphShadeColor{gray}{black}{gray}
- \tikzstyle{EdgeStyle} = [TempEdgeStyle]
- \begin{scope}[rotate=-30]
- \grEmptyCycle[RA=5.4]{3}
- \end{scope}
- \tikzstyle{EdgeStyle}= [TempEdgeStyle,bend right=10]
- \grCycle[prefix=b,RA=4]{12}
- \tikzstyle{EdgeStyle}= [TempEdgeStyle]
- \grCirculant[prefix=c,RA=2]{4}{2}
- \tikzstyle{EdgeStyle}= [TempEdgeStyle,bend left]
- \EdgeDoubleMod{c}{4}{0}{1}%
- {b}{12}{4}{3}{4}
- \tikzstyle{EdgeStyle}= [TempEdgeStyle,bend right]
- \EdgeDoubleMod{c}{4}{0}{1}
- {b}{12}{8}{3}{4}
- \tikzstyle{EdgeStyle}= [TempEdgeStyle]
- \EdgeDoubleMod{a}{3}{0}{1}%
- {b}{12}{11}{4}{3}
- \EdgeDoubleMod{c}{4}{0}{1}%
- {b}{12}{0}{3}{4}
- \tikzstyle{EdgeStyle}= [TempEdgeStyle,bend left=60]
- \EdgeDoubleMod{a}{3}{0}{1}%
- {b}{12}{8}{4}{3}
- \tikzstyle{EdgeStyle}= [TempEdgeStyle,bend right=60]
- \EdgeDoubleMod{a}{3}{0}{1}%
- {b}{12}{2}{4}{3}
- \tikzstyle{EdgeStyle}=[TempEdgeStyle,in=-50,out=-120,
- relative,looseness=2.5]
- \EdgeDoubleMod{a}{3}{0}{1}%
- {b}{12}{5}{4}{3}
- \end{tikzpicture}
-\end{center}
-
-\clearpage\newpage
-Code for the Robertson Graph
-
-\medskip
-\begin{tkzexample}[code only]
-\begin{tikzpicture}[scale=.9]
- \tikzstyle{TempEdgeStyle}= [thick,black,%
- double = gray,%
- double distance = 1.5pt]%
- \SetVertexNoLabel
- \renewcommand*{\VertexBigMinSize}{14pt}
- \GraphInit[vstyle=Shade]
- \SetVertexNoLabel
- \SetUpEdge[style = {thick,%
- double = orange,%
- double distance = 1pt}]
-
- \SetGraphShadeColor{gray}{black}{gray}
- \tikzstyle{EdgeStyle} = [TempEdgeStyle]
- \begin{scope}[rotate=-30]
- \grEmptyCycle[RA=5.4]{3}
- \end{scope}
- \tikzstyle{EdgeStyle}= [TempEdgeStyle,bend right=10]
- \grCycle[prefix=b,RA=4]{12}
- \tikzstyle{EdgeStyle}= [TempEdgeStyle]
- \grCirculant[prefix=c,RA=2]{4}{2}
- \tikzstyle{EdgeStyle}= [TempEdgeStyle,bend left]
- \EdgeDoubleMod{c}{4}{0}{1}%
- {b}{12}{4}{3}{4}
- \tikzstyle{EdgeStyle}= [TempEdgeStyle,bend right]
- \EdgeDoubleMod{c}{4}{0}{1}
- {b}{12}{8}{3}{4}
- \tikzstyle{EdgeStyle}= [TempEdgeStyle]
- \EdgeDoubleMod{a}{3}{0}{1}%
- {b}{12}{11}{4}{3}
- \EdgeDoubleMod{c}{4}{0}{1}%
- {b}{12}{0}{3}{4}
- \tikzstyle{EdgeStyle}= [TempEdgeStyle,bend left=60]
- \EdgeDoubleMod{a}{3}{0}{1}%
- {b}{12}{8}{4}{3}
- \tikzstyle{EdgeStyle}= [TempEdgeStyle,bend right=60]
- \EdgeDoubleMod{a}{3}{0}{1}%
- {b}{12}{2}{4}{3}
- \tikzstyle{EdgeStyle}=[TempEdgeStyle,in=-50,out=-120,
- relative,looseness=2.5]
- \EdgeDoubleMod{a}{3}{0}{1}%
- {b}{12}{5}{4}{3}
- \end{tikzpicture}
-\end{tkzexample}
-
-\clearpage\newpage
-\subsection{\tkzname{Robertson graph with new styles}}
-
-The code with new styles, the result is on the next page.
-
-\bigskip
-\begin{tkzexample}[code only]
- \begin{tikzpicture}[scale=1]
- \GraphInit[vstyle=Art]
- \SetGraphArtColor{gray}{red}
- \begin{scope}[rotate=-30]
- \grEmptyCycle[RA=5]{3}
- \end{scope}
- {\tikzset{EdgeStyle/.append style = {bend right=10}}
- \grCycle[prefix=b,RA=3.5]{12}}
- \grCirculant[prefix=c,RA=2]{4}{2}
- {\tikzset{EdgeStyle/.append style = {bend left}}
- \EdgeDoubleMod{c}{4}{0}{1}%
- {b}{12}{4}{3}{4}}
- {\tikzset{EdgeStyle/.append style = {bend right}}
- \EdgeDoubleMod{c}{4}{0}{1}
- {b}{12}{8}{3}{4}}
- \EdgeDoubleMod{a}{3}{0}{1}%
- {b}{12}{11}{4}{3}
- \EdgeDoubleMod{c}{4}{0}{1}%
- {b}{12}{0}{3}{4}
- {\tikzset{EdgeStyle/.append style = {bend left=60}}
- \EdgeDoubleMod{a}{3}{0}{1}%
- {b}{12}{8}{4}{3}}
- {\tikzset{EdgeStyle/.append style = {bend right=60}}
- \EdgeDoubleMod{a}{3}{0}{1}%
- {b}{12}{2}{4}{3}}
- {\tikzset{EdgeStyle/.append style = {in=-50,out=-120,%
- relative,looseness=2.5}}
- \EdgeDoubleMod{a}{3}{0}{1}%
- {b}{12}{5}{4}{3}}
- \end{tikzpicture}
-\end{tkzexample}
-
-\begin{center}
-\begin{tikzpicture}[scale=1]
-\GraphInit[vstyle=Art]
-\SetGraphArtColor{gray}{red}
-\begin{scope}[rotate=-30]
- \grEmptyCycle[RA=5]{3}
-\end{scope}
-{\tikzset{EdgeStyle/.append style = {bend right=10}}
-\grCycle[prefix=b,RA=3.5]{12}}
-\grCirculant[prefix=c,RA=2]{4}{2}
-{\tikzset{EdgeStyle/.append style = {bend left}}
-\EdgeDoubleMod{c}{4}{0}{1}%
- {b}{12}{4}{3}{4}}
-{\tikzset{EdgeStyle/.append style = {bend right}}
- \EdgeDoubleMod{c}{4}{0}{1}
- {b}{12}{8}{3}{4}}
- \EdgeDoubleMod{a}{3}{0}{1}%
- {b}{12}{11}{4}{3}
- \EdgeDoubleMod{c}{4}{0}{1}%
- {b}{12}{0}{3}{4}
-{\tikzset{EdgeStyle/.append style = {bend left=60}}
- \EdgeDoubleMod{a}{3}{0}{1}%
- {b}{12}{8}{4}{3}}
-{\tikzset{EdgeStyle/.append style = {bend right=60}}
- \EdgeDoubleMod{a}{3}{0}{1}%
- {b}{12}{2}{4}{3}}
- {\tikzset{EdgeStyle/.append style = {in=-50,out=-120,%
- relative,looseness=2.5}}
- \EdgeDoubleMod{a}{3}{0}{1}%
- {b}{12}{5}{4}{3}}
-\end{tikzpicture}
-\end{center}
-\clearpage\newpage
-%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
-%<–––––––––––––––––––– Robertson Wegner –––––––––––––––––––––––––––––––>
-%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
-\begin{NewMacroBox}{grRobertsonWegner}{\oarg{options}\var{$k$}}
-
-\medskip
-From MathWord : \url{http://mathworld.wolfram.com/Robertson-WegnerGraph.html}
-
-\medskip
-\emph{he Robertson-Wegner graph is of the four (5,5)-cage graphs, also called Robertson's cage . Like the other (5,5)-cages, the Robertson-Wegner graph has 30 nodes. It has 75 edges, girth 5, diameter 3, and chromatic number 4.}
-\href{http://mathworld.wolfram.com/Robertson-WegnerGraph.html}%
- {\textcolor{blue}{MathWorld}} by \href{http://en.wikipedia.org/wiki/Eric_W._Weisstein}%
- {\textcolor{blue}{E.Weisstein}}
-
-\end{NewMacroBox}
-
-\subsection{\tkzname{Robertson-Wegner graph}}
-
-\begin{center}
-\begin{tkzexample}[vbox]
-\begin{tikzpicture}[rotate=90,scale=.6]
- \GraphInit[vstyle=Art]
- \tikzset{VertexStyle/.append style={minimum size=2pt}}
- \grRobertsonWegner[RA=6]
- \end{tikzpicture}
-\end{tkzexample}
-\end{center}
-
-The next code gives the same result
-
-\begin{tkzexample}[code only]
-\begin{tikzpicture}[rotate=90]
- \GraphInit[vstyle=Art]
- \grLCF[RA=6]{6,12}{15}
- \EdgeInGraphMod{a}{30}{9}{1}{6} \EdgeInGraphMod*{a}{30}{15}{2}{6}
- \EdgeInGraphMod*{a}{30}{9}{3}{6}
- \end{tikzpicture}
-\end{tkzexample}
-
-
-\endinput \ No newline at end of file