Eigenvalue Characterizations for the Signless Laplacian Spectrum of Weakly Zero-Divisor Graphs on Zn
Year: 2025
Type: article
Abstract: Let R be a commutative ring with identity 1≠0. The weakly zero-divisor graph of R, denoted WΓ(R), is the simple undirected graph whose vertex set consists of the nonzero zero-divisors of R, where two distinct vertices a and b are adjacent if and only if there exist r∈ann(a) and s∈ann(b) such that rs=0. In this paper, we study the signless Laplacian spectrum of WΓ(Zn) for several composite forms of n, including n=p2q2, n=p2qr, n=pmqm and n=pmqr, where p, q, r are distinct primes and m≥2. By using generalized join decomposition and quotient matrix methods, we obtain explicit eigenvalue formulas for each case, along with structural bounds, spectral integrality conditions and Nordhaus–Gaddum-type inequalities. Illustrative examples with computed spectra are provided to validate the theoretical results, demonstrating the interplay between the algebraic structure of Zn and the spectral properties of its weakly zero-divisor graph.
Source: Mathematics
DOI: 10.3390/math13162689
Authors: Nazim, Alaa Altassan, Nof T. Alharbi
Institutions: King Abdulaziz University, Jazan University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W4413375792