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Some classes of perfect strongly annihilating-ideal graphs associated with commutative rings

Mitra Jalali; Abolfazl Tehranian; Reza Nikandish; Hamid Rasouli — 2020

Commentationes Mathematicae Universitatis Carolinae

Let $R$ be a commutative ring with identity and $A (R)$ be the set of ideals with nonzero annihilator. The strongly annihilating-ideal graph of $R$ is defined as the graph $SAG (R)$ with the vertex set $A {(R)}^{*} = A (R) ∖ {0}$ and two distinct vertices $I$ and $J$ are adjacent if and only if $I \cap Ann (J) \neq (0)$ and $J \cap Ann (I) \neq (0)$ . In this paper, the perfectness of $SAG (R)$ for some classes of rings $R$ is investigated.

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