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 $\mathbb{AG}(R)$ 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 {\it et.al.} proved that $\mathbb{AG}({\mathbb{Z}}_n)$ is weakly perfect. In this short paper, we characterize $n$ for which $\mathbb{AG}({\mathbb{Z}}_n)$ is perfect.

arXiv comment9 pages, 0 figures