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