summaryrefslogtreecommitdiff
path: root/obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Levi.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 /obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Levi.tex
parent37cb9bbabbfe1a8d0d1334832814ccbefcf9ac0a (diff)
CTAN sync 202101220300
Diffstat (limited to 'obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Levi.tex')
-rw-r--r--obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Levi.tex79
1 files changed, 0 insertions, 79 deletions
diff --git a/obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Levi.tex b/obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Levi.tex
deleted file mode 100644
index b0d5053f6f..0000000000
--- a/obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Levi.tex
+++ /dev/null
@@ -1,79 +0,0 @@
-\newpage\section{Levi Graph}\label{levi}
-%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
-%<–––––––––––––––––––– Levy –––––––––––––––––––––––––––––––>
-%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
-\begin{NewMacroBox}{grLevi}{\oarg{options}}
-
-\medskip
-
-From Wikipedia \url{http://en.wikipedia.org/wiki/Levi_graph}
-
-\emph{In combinatorics a Levi graph or incidence graph is a bipartite graph associated with an incidence structure. From a collection of points and lines in an incidence geometry or a projective configuration, we form a graph with one vertex per point, one vertex per line, and an edge for every incidence between a point and a line.\hfil\break
-In the mathematical field of graph theory, the Tutte–Coxeter graph or Tutte eight-cage is a 3-regular graph with 30 vertices and 45 edges. As the unique smallest cubic graph of girth 8 it is a cage and a Moore graph. It is bipartite, and can be constructed as the Levi graph of the generalized quadrangle. }
-
-From MathWord : \url{http://mathworld.wolfram.com/LeviGraph.html}
-
-\emph{It has 30 nodes and 45 edges. It has girth 8, diameter 4, chromatic number 2. The Levi graph is a generalized polygon which is the point/line incidence graph of the generalized quadrangle . The graph was first discovered by Tutte (1947), and is also called the Tutte-Coxeter graph , Tutte's cage or "Tutte's (3,8)-cage".The Levi graph is the unique (3,8)-cage graph.\hfil\break
-The incidence graph of a generic configuration is sometimes known as a Levi graph (Coxeter 1950).}
-
-\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}}
-
-Some examples of Levi Graphs with this definition are~:
-\begin{itemize}
-\item Desargues graph
-\item Heawood graph
-\item Heawood graph
-\item Pappus graph
-\item Gray graph
-\item Tutte eight-cage
-\end{itemize}
-
-\end{NewMacroBox}
-
-The two forms can be draw with :
-
- \begin{tkzexample}[code only]
- \grLevi[RA=7]\end{tkzexample}
-
-and
-
- \begin{tkzexample}[code only]
- \grLevi[form=2,RA=7,RB=5,RC=3]\end{tkzexample}
-
-You can see on the next pages, the two forms.
-\vfill\newpage
-Now I show you how to code this graph.
-
-\subsection{\tkzname{Levy graph :form 1}}
-
-\bigskip
-\begin{center}
-\begin{tkzexample}[vbox]
- \begin{tikzpicture}
- \GraphInit[vstyle=Art]
- \grLCF[prefix=a,RA=6]{-13,-9,7,-7,9,13}{5}
- \end{tikzpicture}
-\end{tkzexample}
-\end{center}
-
-
-\vfill\newpage
-
-\subsection{\tkzname{Levy graph :form 2}}
-
-\bigskip
-\begin{center}
-\begin{tkzexample}[vbox]
-\begin{tikzpicture}
- \GraphInit[vstyle=Art]
- \grCycle[prefix=a,RA=7]{10}
- \EdgeInGraphMod{a}{10}{5}
- \grEmptyCycle[prefix=b,RA=5]{10}
- \grEmptyCycle[prefix=c,RA=3]{10}
- \EdgeInGraphMod{c}{10}{4}
- \end{tikzpicture}
-\end{tkzexample}
-\end{center}
-\endinput \ No newline at end of file