On the comaximal ideal graph of a commutative ring

Abstract

Let $R$ be a commutative ring with identity. We use $\Gamma ( R )$ to denote the comaximal ideal graph. The vertices of $\Gamma ( R )$ are proper ideals of R that are not contained in the Jacobson radical of $R$, and two vertices $I$ and $J$ are adjacent if and only if $I + J = R$. In this paper we show some properties of this graph together with the planarity and perfection of $\Gamma ( R )$.