In this paper, we will extend the notion of zero-divisor graph of commutative rings to zero-
divisor graph of abelian groups and study this zero-divisor graph. We characterize the zero …

Let M be an R-module and 0 ¹¦ Î M*= Hom (M, R). The graph G¦(M) is a graph with vertices
Z¦(M)={x Î M\{0}| x¦(y)= 0 or y¦(x)= 0 for some non-zero y Î M}, in which non-zero elements x …

The main idea of the zero-divisor graph of a ring R was first proposed by Beck [1]. He takes
all the elements of Z (R) and x, y∈ Z∗(R) is adjacent if and only if xy= 0. In [2], Anderson and …