A note on comaximal ideal graph of commutative rings

Abstract

Let R be a commutative ring with identity. The comaximal ideal graphG(R) of R is a simple graph with its vertices are the proper ideals of R which are not contained in the Jacobson radical of R, and two vertices I1 and I2 are adjacent if and only if I1+I2=R. In this paper, a dominating set of G(R) is constructed using elements of the center when R is a commutative Artinian ring. Also we prove that the domination number of G(R) is equal to the number of factors in the Artinian decomposition of R. Also, we characterize all commutative Artinian rings(non local rings) with identity for which G(R) is planar.