  Using the new extension of the zero-divisor graph $\widetilde{\Gamma}(R)$
introduced in \cite{Groupe}, we give an approach of the diameter of $\Gamma(R)$
and $\Gamma(R[X])$ other than given in \cite{Lucas} thus we give a complete
characterization for the possible diameters $1$, $2$ or $3$ of $\Gamma(R)$ and
$\Gamma(R[x])$.
