Geodesic
Some classes of perfect strongly annihilating-ideal graphs associated with commutative rings
Commentationes Mathematicae Universitatis Carolinae, Tome 61 (2020) no. 1, pp. 27-34.

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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 ${\rm SAG}(R)$ with the vertex set $A(R)^*=A(R)\setminus\{0\}$ and two distinct vertices $I$ and $J$ are adjacent if and only if $I\cap {\rm Ann}(J)\neq (0)$ and $J\cap {\rm Ann}(I)\neq (0)$. In this paper, the perfectness of ${\rm SAG}(R)$ for some classes of rings $R$ is investigated.
DOI : 10.14712/1213-7243.2020.005
Classification : 05C25, 05C99, 13A15, 13B99
Keywords: strongly annihilating-ideal graph; perfect graph; chromatic number; clique number 
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Jalali, Mitra; Tehranian, Abolfazl; Nikandish, Reza; Rasouli, Hamid. Some classes of perfect strongly annihilating-ideal graphs associated with commutative rings. Commentationes Mathematicae Universitatis Carolinae, Tome 61 (2020) no. 1, pp. 27-34. doi : 10.14712/1213-7243.2020.005. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2020.005/

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