Symmetric graph of a ring with involution

Let R be a ring with involution ∗ . The graph S Γ ∗ ( 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 x y = 0 (or y x = 0 ) and y x ∗ = 0 . The graph S Γ ∗ ( 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.