On signless Laplacian spectrum of weakly zero-divisor graph of commutative ring ℤ𝔫

Let [Formula: see text] be a commutative ring with identity [Formula: see text]. The graph known as the weakly zero-divisor graph of the commutative ring [Formula: see text], denoted as [Formula: see text], is a simple undirected graph whose set of vertices consists of the non-zero zero-divisors of [Formula: see text] and two distinct vertices [Formula: see text] and [Formula: see text] are adjacent if and only if there exist elements [Formula: see text] and [Formula: see text] satisfying the condition [Formula: see text]. The zero-divisor graph of a ring is the spanning subgraph of a weakly zero-divisor graph. In this paper, we find the signless Laplacian spectrum of the weakly zero-divisor graph [Formula: see text]. Specifically, the investigation is carried out on the weakly zero-divisor graph [Formula: see text] for various values of [Formula: see text].