Annihilator intersection graph of a lattice

For a lattice Formula: see text, we associate a graph called the annihilator intersection graph of Formula: see text, denoted by Formula: see text The vertex set of Formula: see text is the set of all nonzero zero-divisors of Formula: see text and any two distinct vertices Formula: see text and Formula: see text are adjacent in Formula: see text if and only if Formula: see text. It has shown that the Formula: see text is disconnected if and only if the number of atoms in Formula: see text is two. If Formula: see text is connected, then we determine the diameter and the girth of Formula: see text We characterize all lattices whose annihilator intersection graph is planar. Further, we obtain the clique number and chromatic number of Formula: see text when Formula: see text is a finite Boolean lattice. We show that the domination number of Formula: see text is not exceeding two. Finally, we obtain a condition under which the annihilator intersection graph is identical with the zero-divisor graph and the annihilator ideal graph of lattices.