On commuting graphs of semisimple rings Original Research Article

Let R be a non-commutative ring. The commuting graph of R denoted by Γ(R), is a graph with vertex set R-45 degree ruleZ(R), and two distinct vertices a and b are adjacent if ab = ba. In this paper we investigate some properties of Γ(R), whenever R is a finite semisimple ring. For any finite field F, we obtain minimum degree, maximum degree and clique number of Γ(Mn(F)). Also it is shown that for any two finite semisimple rings R and S, if Γ(R) similar, equals Γ(S), then there are commutative semisimple rings R1 and S1 and semisimple ring T such that R similar, equals T × R1, S similar, equals T × S1 and midR1mid = midS1mid.