一类互联网络模型

A Class of Interconnection Network Models

设Sn是一个对称群.让n表示{1,2,…,n},B*表示Sn中所有对换的集合.设B是B*的任一子集.关于B的对换图Wn被定义为:顶点集是n,边集是{[uv]:(uv)∈B}.如果Wn是一棵树,则这个对称图称为一棵对换树Tn.Tn是Sn的一个极小生成集.研究了Cayley图Cay(Sn,Tn)的性质,从而说明了这类互连网络模型的优越性.

Let \%S\-\{n\}\% be the symmetric group. Let \%n\% equal \%{1,2,\:,n}, B\+\{*\}\% denote the set of all transpositions for \%S\-\{n\}\% and let \%B\% be any sabset of \%B\+*\%. The transposition graph \%W\-\{n\}\% with respect to \%B\% is defined by taking \%n\% as \%V\%set and \%{\:(uv)∈B}\% as lateral set. A transposition graph is called a transposition tree \%T\-\{n\}\% if \%W\-\{n\}\% is a tree. \%T\-\{n\}\% is a minimal generating set of \%S\-\{n\}\%. In this paper, we study the properties of the Cayley graph Cay\%(S\-n,T\-n)\%. Prove that this model is a nice model.