PERFECTNESS OF THE ANNIHILATOR GRAPH OF ARTINIAN COMMUTATIVE RINGS

‎Let R be a commutative ring and Z(R) be the set of its zero-divisors. The annihilator graph of R, denoted by AG(R) is a simple undirected graph whose vertex set is Z(R) ∗ , the set of all nonzero zero-divisors of R, and two distinct vertices x and y are adjacent if and only if annR(xy) ̸= annR(x) ∪ annR(y). In this paper, perfectness of the annihilator graph for some classes of rings is investigated. More precisely, we show that if R is an Artinian ring, then AG(R) is perfect.