ON THE COMMUTING GRAPH FOR DIRECT PRODUCT OF NON-COMMUTATIVE RINGS

Let R be a non-commutative ring with unity. The commuting graph of R denoted by ?(R) is a graph with vertex set R\ Z(R) and two vertices a and b are adjacent if ab = ba. In this paper we investigate some properties of ?(R1×R2), where R1 and R2 are two finite non-commutative rings. Also we obtain maximum degree, independence number and clique number of ?(R1×