A NOTE ON THE ZERO DIVISOR GRAPH OF A LATTICE

Let l be a lattice with the least element 0. an element x 2 l is a zero divisor if x^y = 0for some y 2 l = l n f0g. the set of all zero divisors is denoted by z(l). we associate a simplegraph ??(l) to l with vertex set z(l) = z(l) n f0g, the set of non-zero zero divisors of l and distinctx; y 2 z(l) are adjacent if and only if x ^ y = 0. in this paper, we obtain certain properties anddiameter and girth of the zero divisor graph ??(l). also we nd a dominating set and the dominationnumber of the zero divisor graph ??(l).