  In this paper, we study the zero divisor graph $\Gamma^m(L)$ of a
multiplicative lattice L. We prove under certain conditions that for a reduced
multiplicative lattice L having more than two minimal prime elements,
$\Gamma^m(L)$ contains a cycle and $gr(\Gamma^m(L)) = 3$. This essentially
proves that for a reduced ring R with more than two minimal primes,
$gr(\mathbb{AG}(R))) = 3$ which settles the conjecture of Behboodi and Rakeei
[9]. Further, we have characterized the diameter of $\Gamma^m(L)$.
