Dominating Sets of the Annihilating-Ideal Graphs

Let R be a commutative ring with identity and A(R) be the set of ideals with non-zero annihilator. The annihilating-ideal graph of R is defined as the graph AG(R) with the vertex set A(R)⁎=A(R)\{0} and two distinct vertices I and J are adjacent if and only if IJ=0. In this paper, we study the domination number of AG(R) and some connections between the domination numbers of annihilating-ideal graphs and zero-divisor graphs are given.