Some classes of perfect strongly annihilating-ideal graphs associated with commutative rings

Abstract

. Let R be a commutative ring with identity and A ( R ) be the set of ideals with nonzero annihilator. The strongly annihilating-ideal graph of R is defined as the graph SAG( R ) with the vertex set A ( R ) ∗ = A ( R ) \ { 0 } and two distinct vertices I and J are adjacent if and only if I ∩ Ann( J ) 6 = (0) and J ∩ Ann( I ) 6 = (0). In this paper, the perfectness of SAG( R ) for some classes of rings R is investigated.