@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}
}