Shahrood University of Technology Journal of Algebraic Systems 2345-5128 10 2 2023 01 01 PERFECTNESS OF THE ANNIHILATOR GRAPH OF ARTINIAN COMMUTATIVE RINGS 335 343 2478 10.22044/jas.2022.11358.1571 EN M. Adlifard Department of Mathematics, Roudbar Branch, Islamic Azad University, Roudbar, Iran. Sh. Payrovi Department of Mathematics, Imam Khomeini International University, P.O. Box 34149-1-6818, Qazvin, Iran. Journal Article 2021 11 03 ‎Let $R$ be a commutative ring and $Z(R)$ be the set of its zero-divisors‎.<br />‎The annihilator graph of $R$‎, ‎denoted by $AG(R)$ is a simple undirected graph whose vertex‎<br />‎set is $Z(R)^*$‎, ‎the set of all nonzero zero-divisors of $R$‎, ‎and two distinct vertices $x$ and‎<br />‎$y$ are adjacent if and only if ${\rm ann}_R(xy)\neq {\rm ann}_R(x)\cup {\rm ann}_R(y)$‎.<br />‎In this paper‎, ‎perfectness of the annihilator graph for some classes of rings is investigated‎.<br />‎More precisely‎, ‎we show that if $R$ is an Artinian ring‎, ‎then $AG(R)$ is perfect‎. https://jas.shahroodut.ac.ir/article_2478_e39eb81cb204b26ca17a13df1e6c0f32.pdf