### On Perfect Co-Annihilating-Ideal Graph of a Commutative Artinian Ring

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**Authors: ** S. M. S. MIRGHADIM, M. J. NIKMEHR AND R. NIKANDISH

**DOI: ** 10.46793/KgJMat2101.063M

**Abstract: **

Let R be a commutative ring with identity. The co-annihilating-ideal graph of R, denoted by A_{R}, is a graph whose vertex set is the set of all non-zero proper ideals of R and two distinct vertices I and J are adjacent whenever Ann(I) ∩ Ann(J) = (0). In this paper, we characterize all Artinian rings for which both of the graphs A_{R} and A_{R} (the complement of A_{R}), are chordal. Moreover, all Artinian rings whose A_{R} (and thus A_{R}) is perfect are characterized.

**Keywords: **

Co-annihilating-ideal graph, perfect graph, chordal graph.

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