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

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Zero divisor Mathematics Combinatorics Commutative ring Simple graph Vertex (graph theory) Modulo Graph Zero (linguistics) Discrete mathematics Commutative property Linguistics Philosophy

Bilal Ahmad Rather , S. Pirzada , T. A. Naikoo , Yilun Shang ·

YOU? · · 2021 · Open Access · · DOI: https://doi.org/10.3390/math9050482 · OA: W3133494522

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.

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

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