On a new extension of the zero-divisor graph (II)

Abstract

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).