%0 Journal Article
%T A Note on a graph associated to a commutative ring
%J Journal of Algebra and Related Topics
%I University of Guilan
%Z 2345-3931
%A Visweswaran, S.
%A Parejiya, J.
%D 2017
%\ 06/01/2017
%V 5
%N 1
%P 61-82
%! A Note on a graph associated to a commutative ring
%K Comaximal graph of a ring
%K complete graph
%K chromatic number
%K clique number
%K planar graph
%R 10.22124/jart.2017.2399
%X 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 $Rxcap Ry = Rxy$. 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.
%U https://jart.guilan.ac.ir/article_2399_1591422012d4680950f3bb1760b533a6.pdf