مشخصات پژوهش

Let R be a commutative ring with non-zero identity. The annihilator- inclusion ideal graph of R, denoted by R, is a graph whose vertex set is the of all non-zero proper ideals of R and two distinct vertices I and J are adjacent if and only if either Ann(I)  J or Ann(J)  I. The purpose of this paper is to provide some basic properties of the graph R. In particular, shows that R is a connected graph with diameter at most three, and has girth 3 or 1. Furthermore, is determined all isomorphic classes of non-local Artinian rings whose annihilator-inclusion ideal graphs have genus zero or one.