Coidempotent graph of a ring

Abstract

Let [Formula: see text] be a ring with nonzero identity. The coidempotent graph of [Formula: see text], denoted it 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] are adjacent in [Formula: see text] if and only if [Formula: see text] or [Formula: see text] is an idempotent of [Formula: see text]. In this paper, we study some basic properties of [Formula: see text] and find some results about the ring-theoretic properties of [Formula: see text] and graph-theoretic properties of [Formula: see text].