On Perfectness of Annihilating-Ideal Graph of $\mathbb{Z}_n$

Abstract

The annihilating-ideal graph of a commutative ring R with unity is defined as the graph AG(R) with the vertex set is the set of all non-zero ideals with non-zero annihilators and two distinct vertices I and J are adjacent if and only if IJ = 0. Nikandish et.al. proved that AG(Z n ) is weakly perfect. In this short paper, we characterize n for which AG(Z n ) is perfect.