Geodesic
On Perfect Co-Annihilating-Ideal Graph of a Commutative Artinian Ring
Kragujevac Journal of Mathematics, Tome 45 (2021) no. 1, p. 63

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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 $\mathrm{Ann}(I)\cap \mathrm{Ann}(J)=(0)$. In this paper, we characterize all Artinian rings for which both of the graphs $A_R$ and $\overline{A_R}$ (the complement of $A_R$), are chordal. Moreover, all Artinian rings whose $A_R$ (and thus $\overline{A_R}$) is perfect are characterized.
Classification : 05C19 05C75, 05C25
Keywords: co-annihilating-ideal graph, perfect graph, chordal graph 
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     title = {On {Perfect} {Co-Annihilating-Ideal} {Graph} of a {Commutative} {Artinian} {Ring}},
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S. M. Saadat Mirghadim; M. J. Nikmehr; R. Nikandish. On Perfect Co-Annihilating-Ideal Graph of a Commutative Artinian Ring. Kragujevac Journal of Mathematics, Tome 45 (2021) no. 1, p. 63 . http://geodesic.mathdoc.fr/item/KJM_2021_45_1_a4/