@article { author = {Purohit, Krishna and Parejiya, Jaydeep and Parsania, Mahesh}, title = {Some Remarks on $(\operatorname{INC}(R))^{c}$}, journal = {Algebraic Structures and Their Applications}, volume = {9}, number = {2}, pages = {181-198}, year = {2022}, publisher = {Yazd University}, issn = {2382-9761}, eissn = {2423-3447}, doi = {10.22034/as.2022.2728}, abstract = {Let $R$ be a commutative ring with identity $1 \neq 0$ which admits atleast 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 $I_{1}$ and $I_{2}$ are joined by an edge in $(\operatorname{INC}(R))^{c}$ if and only if $I_{1} \subseteq I_{2}$ or $I_{2} \subseteq I_{1}$. In this article, we have studied some interesting properties of $(\operatorname{INC}(R))^{c}$.}, keywords = {$(operatorname{INC}(R))^{c}$,Maximal ideal, SPIR}, url = {https://as.yazd.ac.ir/article_2728.html}, eprint = {https://as.yazd.ac.ir/article_2728_f39a6f6a24600b29ee4c547dbc9f4923.pdf} }