summaryrefslogtreecommitdiff
path: root/obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Cage.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-Cage.tex
parent37cb9bbabbfe1a8d0d1334832814ccbefcf9ac0a (diff)
CTAN sync 202101220300
Diffstat (limited to 'obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Cage.tex')
-rw-r--r--obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Cage.tex43
1 files changed, 0 insertions, 43 deletions
diff --git a/obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Cage.tex b/obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Cage.tex
deleted file mode 100644
index 520b38555f..0000000000
--- a/obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Cage.tex
+++ /dev/null
@@ -1,43 +0,0 @@
-\newpage\section{Cage}\label{cage}
-%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
-%<–––––––––––––––––––– Cage –––––––––––––––––––––––––––––––>
-%<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
-\begin{NewMacroBox}{Cage Graphs}{}
-
-\medskip
-From Wikipedia \url{http://en.wikipedia.org/wiki/Cage_(graph_theory)}\\
-\emph{In the mathematical area of graph theory, a cage is a regular graph that has as few vertices as possible for its girth.\\
-Formally, an $(r,g)$-graph is defined to be a graph in which each vertex has exactly $r$ neighbors, and in which the shortest cycle has length exactly $g$. It is known that an $(r,g)$-graph exists for any combination of $r \geq 2$ and $g \geq 3$. An $(r,g)$-cage is an $(r,g)$-graph with the fewest possible number of vertices, among all $(r,g)$-graphs.}
-
-\medskip
-From MathWorld \url{http://mathworld.wolfram.com/CageGraph.html}\\
-\emph{A $(r,g)$-cage graph is a $v$-regular graph of girth $g$ having the minimum possible number of nodes. When $v$ is not explicitly stated, the term "$g$-cage" generally refers to a $(3,g)$-cage.}
-\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}}
-
-\medskip
-Examples :
-
-\medskip
-\begin{tabular}{ll}
- \bottomrule
-$(r,g)$ & Names \\
-\midrule
-$(3,3)$ & complete graph $K_4$ \\
-$(3,4)$ & complete bipartite graph $K_{3,3}$ Utility Graph\ref{bipart} \\
-$(3,5)$ & Petersen graph \ref{petersen} \\
-$(3,6)$ & Heawood graph \ref{heawood} \\
-$(3,7)$ & McGee graph \ref{mcgee} \\
-$(3,8)$ & Levi graph \ref{levi} \\
-$(3,10)$ & Balaban 10-cage \ref{balaban} \\
-$(3,11)$ & Balaban 11-cage \ref{balaban} \\
-$(3,12)$ & Tutte 12-cage \\
-$(4,3)$ & complete graph $K_5$ \\
-$(4,4)$ & complete bipartite graph $K_{4,4}$ \ref{bipart} \\
-$(4,5)$ & Robertson graph\ref{robertson} \\
-$(4,6)$ & Wong (1982)\ref{wong} \\
-\end{tabular}
-\end{NewMacroBox}
-
-\endinput \ No newline at end of file