M. Adlifard - Department of Mathematics, Roudbar Branch Islamic Azad University, Roudbar, Iran
Sh. Payrovi - Department of Mathematics, Imam Khomeini International University, Qazvin, Iran

Let R be a commutative ring and let \Bbb A(R) bethe set of all ideals of R with nonzero annihilator.The annihilator-ideal graph of R is defined as the graph{A_I}(R) with the vertex set \Bbb A(R)^*=\Bbb A(R)\setminus\{۰\} and twodistinct vertices I and J are adjacent if and only if{\rm Ann}_R(IJ)\neq{\rm Ann}_R(I) \cup{\rm Ann}_R(J). In this paper, perfectness of{A_I}(R) for some classes of rings is investigated.

‎Annihilator-ideal graph‎, ‎Perfect graph‎, ‎Chromatic number‎, ‎Clique number