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diff --git a/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Robertson.tex b/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Robertson.tex new file mode 100644 index 0000000000..ce8807ce0b --- /dev/null +++ b/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Robertson.tex @@ -0,0 +1,243 @@ +\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
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