summaryrefslogtreecommitdiff
path: root/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Robertson.tex
diff options
context:
space:
mode:
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-Robertson.tex
parent37cb9bbabbfe1a8d0d1334832814ccbefcf9ac0a (diff)
CTAN sync 202101220300
Diffstat (limited to 'macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Robertson.tex')
-rw-r--r--macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Robertson.tex243
1 files changed, 243 insertions, 0 deletions
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 \ No newline at end of file