On Seidel Laplacian spectrum of the zero-divisor graph over ℤn

Consider a commutative ring denoted as [Formula: see text], and let [Formula: see text] represent its set of zero-divisors. The zero-divisor graph of [Formula: see text], symbolized as [Formula: see text], is a type of undirected graph characterized by its vertex set, [Formula: see text]. Within this graph, two distinct vertices, labeled as [Formula: see text] and [Formula: see text], are linked by an edge if and only if their product, [Formula: see text]. This article delves into the exploration of Seidel Laplacian eigenvalues in the context of the graphs [Formula: see text], with a specific focus on instances where [Formula: see text] and [Formula: see text]. Here, [Formula: see text] and [Formula: see text], represent distinct prime numbers, with [Formula: see text] being less than [Formula: see text], while [Formula: see text] is a positive integer. As consequences of our main theorems, several known results can be either generalized or deduced.