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

Abstract

We continue our study of the new extension of zero-divisor graph. We give a complete characterization for the possible diameters of $\tilde{\Gamma }(R)$ and $\tilde{\Gamma }(R[x_1,\dots ,x_n])$, we investigate the relation between the zero-divisor graph, the subgraph of total graph on $Z(R{)}^{\star }$ and $\tilde{\Gamma }(R)$ and we present some other properties of $\tilde{\Gamma }(R)$.