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 I J = 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.