@article { author = {Visweswaran, S. and Vadhel, P.}, title = {Some results on a subgraph of the intersection graph of ideals of a commutative ring}, journal = {Journal of Algebra and Related Topics}, volume = {6}, number = {2}, pages = {35-61}, year = {2018}, publisher = {University of Guilan}, issn = {2345-3931}, eissn = {2382-9877}, doi = {10.22124/jart.2018.11188.1114}, abstract = {The rings considered in this article are commutative with identity which admit at least one nonzero proper ideal.   Let $R$ be a ring. Let us denote  the collection  of all proper ideals  of $R$ by $\mathbb{I}(R)$  and $\mathbb{I}(R)\backslash \{(0)\}$ by $\mathbb{I}(R)^{*}$.  With $R$, we associate an undirected graph denoted by $g(R)$, whose vertex set is $\mathbb{I}(R)^{*}$ and distinct vertices $I_{1}, I_{2}$ are adjacent in $g(R)$  if and only if $I_{1}\cap I_{2}\neq I_{1}I_{2}$.  The aim of this article is to study the interplay between the graph-theoretic properties of $g(R)$ and the ring-theoretic properties of $R$.}, keywords = {Artinian ring,Special principal ideal ring,diameter,girth,clique number}, url = {https://jart.guilan.ac.ir/article_3328.html}, eprint = {https://jart.guilan.ac.ir/article_3328_37da989245b3ff3ca164523e990de30b.pdf} }