%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 $Rx\cap Ry = Rxy$.  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. %U https://jart.guilan.ac.ir/article_2399_1591422012d4680950f3bb1760b533a6.pdf