Work

On Laplacian Eigenvalues of the Zero-Divisor Graph Associated to the Ring of Integers Modulo n

Year: 2021

Type: article

Abstract: Given a commutative ring R with identity 1≠0, let the set Z(R) denote the set of zero-divisors and let Z*(R)=Z(R)∖{0} be the set of non-zero zero-divisors of R. The zero-divisor graph of R, denoted by Γ(R), is a simple graph whose vertex set is Z*(R) and each pair of vertices in Z*(R) are adjacent when their product is 0. In this article, we find the structure and Laplacian spectrum of the zero-divisor graphs Γ(Zn) for n=pN1qN2, where p<q are primes and N1,N2 are positive integers.

Source: Mathematics

DOI: 10.3390/math9050482

Authors: Bilal A. Rather, Shariefuddin Pirzada, Tariq A. Naikoo, Yilun Shang

Institutions: University of Kashmir, Islamia College of Science and Commerce, Srinagar, Northumbria University

Language: English

Topic: Graph theory and applications

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,728

Funders: Department of Science and Technology, Ministry of Science and Technology, India, Science and Engineering Research Board