A note on a graph related to the comaximal ideal graph of a commutative ring

  ‎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 Inotsubseteq 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.