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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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.

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