A graph with respect to idempotents of a ring

Abstract

Let [Formula: see text] be a ring with nonzero identity. The Idempotent graph of [Formula: see text], denoted by [Formula: see text], has its set of vertices equal to the set of all elements of [Formula: see text]; Distinct vertices [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text] is an idempotent of [Formula: see text]. In this paper, we study some basic properties of [Formula: see text] such as connectedness, diameter and girth.