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.