Some results on the complement of the weakly zero-divisor graph of a reduced ring

The rings considered in this paper are commutative with identity that admit at least one nonzero zero-divisor. Let [Formula: see text] be a ring. We denote the set of all zero-divisors of [Formula: see text] by [Formula: see text] and [Formula: see text] by [Formula: see text]. The weakly zero-divisor graph of [Formula: see text], denoted by [Formula: see text], is an undirected graph whose vertex set is [Formula: see text] and distinct vertices [Formula: see text] and [Formula: see text] are adjacent if and only if there exist [Formula: see text] and [Formula: see text] such that [Formula: see text]. We denote the complement of [Formula: see text] by [Formula: see text]. With the assumption that [Formula: see text] is reduced, this paper aims to discuss some results on the basic properties of [Formula: see text] and study the interplay between some graph-theoretic properties of [Formula: see text] and the ring-theoretic properties of [Formula: see text].