On the domination of the essential ideal graph of a commutative ring

Let A be a commutative ring with nonzero unity. The essential ideal graph of A, ℰA, is a graph with set of all nonzero proper ideals of A as the vertex set and two vertices I and J are adjacent whenever I+J is an essential ideal. In this article, we discuss about the domination number of the essential ideal graph of a commutative ring. We obtain a characterization for reduced rings to have the domination number 1. Also, we determine the domination parameters of essential ideal graph of the commutative rings ℤn and F1 × F2 × ··· × Fn, n ≥ 2.