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 vertexset is Z (R) ^*, the set of all nonzero zero-divisors of R, and two distinct vertices x andy 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.
Adlifard et al. (Sun,) studied this question.
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