Some Remarks on (\operatorname{INC}(R))^{c}

Let R be a commutative ring with identity ۱ \neq ۰ which admits at least two maximal ideals. In this article, we have studied simple, undirected graph (\operatorname{INC}(R))^{c} whose vertex set is the set of all proper ideals which are not contained in J(R) and two distinct vertices I_{۱} and I_{۲} are joined by an edge in (\operatorname{INC}(R))^{c} if and only if I_{۱} \subseteq I_{۲} or I_{۲} \subseteq I_{۱}. In this article, we have studied some interesting properties of (\operatorname{INC}(R))^{c}.

Keywords:

(operatorname{INC}(R))^{c} , Maximal ideal , SPIR