On the dominating sets of the complement of the annihilating ideal graph of a commutative ring

Abstract

Let R be a commutative ring with identity which is not an integral domain. Let A(R)^∗ denote the collection of all nonzero annihilating ideals of R and AG(R) denote the annihilating ideal graph of R. In this article, we consider the dominating sets of (AG(R))^c (where (AG(R))^c is the complement of AG(R)) and study the influence of the dominating sets of (AG(R))^c on the ring structure of R and vice-versa.