Abstract
Let R be a ring with involution *. The graph S Gamma* ( R) is obtained by letting all the elements of nonzero zero-divisors of R to be the vertices and defining distinct vertices x and y to be adjacent if xy = 0 (or yx = 0) and yx* = 0. The graph S Gamma* (R) is a generalization of the well known zero-divisor graph of R. In this paper, some graph theoretical properties of the *-symmetric graph are studied.