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 AR, 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 AR and AR (the complement of AR), are chordal. Moreover, all Artinian rings whose AR (and thus AR) is perfect are characterized.
Keywords:
Co-annihilating-ideal graph, perfect graph, chordal graph.
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