الملخص

Let R be a commutative ring with identity and AG(R) be the set of ideals with      non-zero annihilators. The annihilating ideal graph AG(R) is a graph of vertex set             AG (R)\{(0)}  and two distinct ideal vertices I  and J are adjacent if and only if  . In this paper , we establish a new fundamental properties of AG(R) as well as its connection with Γ(R).