diff options
author | Norbert Preining <norbert@preining.info> | 2021-01-22 03:00:46 +0000 |
---|---|---|
committer | Norbert Preining <norbert@preining.info> | 2021-01-22 03:00:46 +0000 |
commit | e1a7798f45cd37c0aa0bfaaef5f0acb4e48bc867 (patch) | |
tree | d2bbebcdb7bcb8fe013a9d3cbd2cff880b18afbf /obsolete/macros/latex/contrib/tkz/tkz-berge/NamedGraphs/doc/latex/NamedGraphs-Cage.tex | |
parent | 37cb9bbabbfe1a8d0d1334832814ccbefcf9ac0a (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.tex | 43 |
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 |