A generalization of the cozero-divisor graph of a commutative ring

Let [Formula: see text] be a commutative ring with identity and [Formula: see text] be an ideal of [Formula: see text]. The zero-divisor graph of [Formula: see text] with respect to [Formula: see text], denoted by [Formula: see text], is the graph whose vertices are the set [Formula: see text] with distinct vertices [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text]. The cozero-divisor graph [Formula: see text] of [Formula: see text] is the graph whose vertices are precisely the non-zero, non-unit elements of [Formula: see text] and two distinct vertices [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text] and [Formula: see text]. In this paper, we introduced and investigated a new generalization of the cozero-divisor graph [Formula: see text] of [Formula: see text] denoted by [Formula: see text]. In fact, [Formula: see text] is a dual notion of [Formula: see text].