##### 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 vertex‎‎set is $Z(R)^*$‎, ‎the set of all nonzero zero-divisors of $R$‎, ‎and two distinct vertices ...  Read More
‎Let $R$ be a commutative ring and $M$ be an $R$-module‎. ‎The‎ ‎annihilator graph of $M$‎, ‎denoted by $AG(M)$ is a simple undirected‎ ‎graph associated to $M$ whose the set of vertices is‎ ‎$Z_R(M) \setminus {\rm Ann}_R(M)$ and two distinct vertices $x$ and‎ ...  Read More