On commuting graphs of semisimple rings

Let R be a non-commutative ring. The commuting graph of R denoted by Gamma(R), is a graph with vertex set R \ Z(R), and two distinct vertices a and b are adjacent if ab = ba. In this paper we investigate some properties of Gamma(R), whenever R is a finite semisimple ring. For any finite field F, we obtain minimum degree, maximum degree and clique number of Gamma(M-n, (F)). Also it is shown that for any two finite semisimple rings R and S, if Gamma(R) similar or equal to Gamma(S), then there are commutative semisimple rings R-1 and S-1 and semisimple ring T such that R similar or equal to T x R-1, S similar or equal to T x S-1 and \R-1\ = \S-1\. (C) 2004 Elsevier Inc. All rights reserved.