\newpage\section{Cocktail Party graph}\label{cocktail} %<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> %<––––––––––––––––––––––––––––– Cocktail Party –––––––––––––––––––––––––––> %<––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> \begin{NewMacroBox}{grCocktailParty}{\oarg{options}\var{integer}} \medskip From MathWord : \url{http://mathworld.wolfram.com/CocktailPartyGraph.html} \emph{The cocktail party graph of order , also called the hyperoctahedral graph (Biggs 1993, p. 17) is the graph consisting of two rows of paired nodes in which all nodes but the paired ones are connected with a graph edge. It is the graph complement of the ladder graph , and the dual graph of the hypercube graph.\hfill\break This graph arises in the handshake problem. It is a complete n-partite graph that is denoted by Brouwer et al. (1989, pp. 222-223), and is distance-transitive, and hence also distance-regular.\hfill\break The cocktail party graph of order is isomorphic to the circulant 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}} \medskip The Chvátal graph is implemented in \tkzname{tkz-berge} as \tkzcname{grCocktailParty} with two forms. \end{NewMacroBox} \subsection{\tkzname{Cocktail Party graph form 1 }} \tikzstyle{VertexStyle} = [shape = circle, shading = ball,% ball color = green,% minimum size = 24pt,% draw] \SetVertexMath \tikzstyle{EdgeStyle} = [thick,% double = orange,% double distance = 1pt] \begin{center} \begin{tkzexample}[vbox] \begin{tikzpicture} \grCocktailParty[RA=3,RS=5]{4} \end{tikzpicture} \end{tkzexample} \end{center} \vfill\newpage \subsection{\tkzname{Cocktail Party graph form 2 }} \vspace*{2cm} \begin{center} \begin{tkzexample}[vbox] \begin{tikzpicture} \grCocktailParty[form=2,RA=4,RS=6]{4} \end{tikzpicture} \end{tkzexample} \end{center} \endinput