The co-annihilating graph of a commutative ring

Abstract

Let [Formula: see text] be a commutative ring with identity and [Formula: see text] be the set of all non-zero non-units of [Formula: see text]. The co-annihilating graph of [Formula: see text], denoted by [Formula: see text], is a graph with vertex set [Formula: see text] and two vertices [Formula: see text] and [Formula: see text] are adjacent whenever [Formula: see text]. In this paper, we initiate the study of the co-annihilating graph of a commutative ring and we investigate its properties.