%0 Journal Article %T A note on a graph related to the comaximal ideal graph of a commutative ring %J Algebraic Structures and Their Applications %I Yazd University %Z 2382-9761 %A Visweswaran, Subramanian %A Parejiya, Jaydeep %D 2017 %\ 02/01/2017 %V 4 %N 1 %P 57-76 %! A note on a graph related to the comaximal ideal graph of a commutative ring %K Comaximal ideal graph of a commutative ring %K Complete graph %K von Neumann regular ring %K bipartite graph %K Clique number %R 10.22034/as.2017.1123 %X  ‎The rings considered in this article are commutative with identity which admit at least two maximal ideals‎.  ‎This article is inspired by the work done on the comaximal ideal graph of a commutative ring‎. ‎Let R be a ring‎.  ‎We associate an undirected graph to R denoted by \mathcal{G}(R)‎,  ‎whose vertex set is the set of all proper ideals I of R such that I\not\subseteq J(R)‎, ‎where J(R) is the Jacobson radical of R  and distinct vertices I1‎, ‎I2are adjacent in \mathcal{G}(R) if and only if I1∩ I2 = I1I2‎.  ‎The aim of this article is to study the interplay between the graph-theoretic properties of \mathcal{G}(R) and the ring-theoretic properties of R. %U https://as.yazd.ac.ir/article_1123_02c4c66101785f6e69330945831e4fce.pdf