The graph of equivalence classes of zero-divisors of a poset

In this paper, we give the definition of the graph of equivalence classes of zero-divisors of a poset P. We prove that if [a] has maximal degree in V(γE(P)), then ann(a) is maximal in Anih(P). Also, we give some other properties of the graph γE(P). Moreover, we characterize the cut vertices of γE(P) and study the cliques of these graphs