Total graph of the ring Z(n) x Z(m)

Let R be a commutative ring and Z(R) be the set of all zero-divisors of R. The total graph of R, denoted by T-Gamma(R), is the (undirected) graph with vertices set R. For any two distinct elements x, y is an element of R, the vertices x and y are adjacent if and only if x + y is an element of Z(R). In this paper, we obtain certain fundamental properties of the total graph of Z(n) x Z(m), where n and m are positive integers. We determine the clique number and independent number of the total graph T-Gamma(Z(n) x Z(m)).