Some properties of comaximal ideal graph of a commutative ring

Abstract

Let $R$ be a commutative ring with identity‎. ‎We use‎ ‎$varphi (R)$ to denote the comaximal ideal graph‎. ‎The vertices‎ ‎of $varphi (R)$ are proper ideals of R which 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 planarity of line graph‎ ‎associated to $varphi (R)$‎.