@article {
author = {Visweswaran, S. and Parejiya, J.},
title = {A Note on a graph associated to a commutative ring},
journal = {Journal of Algebra and Related Topics},
volume = {5},
number = {1},
pages = {61-82},
year = {2017},
publisher = {University of Guilan},
issn = {2345-3931},
eissn = {2382-9877},
doi = {10.22124/jart.2017.2399},
abstract = {The rings considered in this article are commutative with identity. This article is motivated by the work on comaximal graphs of rings. In this article, with any ring $R$, we associate an undirected graph denoted by $G(R)$, whose vertex set is the set of all elements of $R$ and distinct vertices $x,y$ are joined by an edge in $G(R)$ if and only if $Rx\cap Ry = Rxy$. In Section 2 of this article, we classify rings $R$ such that $G(R)$ is complete and we also consider the problem of determining rings $R$ such that $\chi(G(R)) = \omega(G(R))< \infty$. In Section 3 of this article, we classify rings $R$ such that $G(R)$ is planar.},
keywords = {Comaximal graph of a ring,complete graph,chromatic number,clique number,planar graph},
url = {https://jart.guilan.ac.ir/article_2399.html},
eprint = {https://jart.guilan.ac.ir/article_2399_1591422012d4680950f3bb1760b533a6.pdf}
}