In this paper, we introduce a new graph whose vertices are the non-zero zero-divisors of a commutative ring R, and for distincts elements x and y in the set Z(R)* of the non-zero zero-divisors of R, x and y are adjacent if and only if xy = 0 or x + y ∈ Z(R). We present some properties and examples of this graph, and we study its relationship with the zero-divisor graph and with a subgraph of the total graph of a commutative ring.

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We continue our study of the new extension of zero-divisor graph introduced in [5]. We give a complete characterization for the possible diameters of Γ(R) and Γ(R[x 1 , . . . , x n ]), we investigate the relation between the zero-divisor graph, the subgraph of total graph on Z(R) ⋆ and Γ(R) and we present some other properties of Γ(R).