# On perfectness of annihilating-ideal graph of $\mathbb{Z}_n$

Document Type : Original paper

Authors

1 Presidency University, Kolkata

2 Department of Mathematics, Presidency University, Kolkata

Abstract

The annihilating-ideal graph of a commutative ring $R$ with unity is defined as the graph $AG(R)$ whose 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 $AG(\mathbb{Z}_n)$ is weakly perfect. In this short paper, we characterize $n$ for which $AG(\mathbb{Z}_n)$ is perfect.

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