On the Spectrum of Generalized Zero-Divisor Graph of the Ring \(Z_p^α q^β\)
The generalized zero-divisor graph of a commutative ring \(R\), denoted by \(Γ’(R)\), is a simple (undirected) graph with vertex set \(Z^*(R)\), the set of all nonzero zero-divisors of \(R\) and two distinct vertices \(x\) and \(y\) are adjacent if \(x^ny=0\) or \(y^nx=0\), for some positive integer \(n\). In this paper, we determine the adjacency spectrum of \(Γ’(Z_p^αq^β )\), where \(p,q\) are distinct primes and \(α, β\) are positive integers. Also, we obtain the clique number, stability number, diameter, and the girth of \(Γ’(Z_p^αq^β )\). , number=3, journal=Communications in Mathematics and Applications, author=Lande, Anita and Khairnar, Anil, year=2024, month=Nov., pages=1031–1044