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

Rather, Bilal A., Pirzada, Shariefuddin, Naikoo, Tariq A. and Shang, Yilun (2021) On Laplacian Eigenvalues of the Zero-Divisor Graph Associated to the Ring of Integers Modulo n. Mathematics, 9 (5). p. 482. ISSN 2227-7390

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Official URL: https://doi.org/10.3390/math9050482

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.

Item Type: Article
Additional Information: Funding information: This research received no external funding. The research of S. Pirzada is supported by the SERB-DST research project number MTR/2017/000084.
Uncontrolled Keywords: laplacian matrix; zero-divisor graph; integers modulo ring; gaussian integer ring; Eulers’s totient function
Subjects: G100 Mathematics
Department: Faculties > Engineering and Environment > Computer and Information Sciences
Depositing User: Elena Carlaw
Date Deposited: 26 Feb 2021 10:23
Last Modified: 31 May 2021 14:42
URI: http://nrl.northumbria.ac.uk/id/eprint/45548

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