Mitra Jalali, Abolfazl Tehranian, Reza Nikandish, Hamid Rasouli
Some classes of perfect strongly annihilating-ideal graphs associated with commutative rings

Comment.Math.Univ.Carolin. 61,1 (2020) 27-34.

Abstract: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.

Keywords: strongly annihilating-ideal graph; perfect graph; chromatic number; clique number

DOI: DOI 10.14712/1213-7243.2020.005
AMS Subject Classification: 13A15 13B99 05C99 05C25