The non-zero divisor graph of a ring

Let R be a ring, we associate a simple graph Phi(R) to R, with vertices V(R) = R\{0, 1, -1}, where distinct vertices x, y is an element of V(R) are adjacent if and only if either xy not equal 0 or yx not equal 0. In this paper, we prove that if Phi(R) is connected such that R not congruent to Z(2) x Z(4) then the diameter of Phi(R) is almost 2. Also, we will pay specific attention to investigate the connectivity of certain rings such that, the ring of integers modulo n, Z(n) is connected, reduced ring and matrix ring.