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

Bilal A. Rather, Shariefuddin Pirzada, Tariq A. Naikoo and Yilun Shang
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Bilal A. Rather: Department of Mathematics, University of Kashmir, Srinagar 190006, India
Shariefuddin Pirzada: Department of Mathematics, University of Kashmir, Srinagar 190006, India
Tariq A. Naikoo: Department of Mathematics, Islamia College of Science and Commerce, Srinagar 190003, India
Yilun Shang: Department of Computer and Information Sciences, Northumbria University, Newcastle NE1 8ST, UK

Mathematics, 2021, vol. 9, issue 5, 1-17

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 ? ( 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 ? ( Z n ) for n = p N 1 q N 2 , where p < q are primes and N 1 , N 2 are positive integers.

Keywords: laplacian matrix; zero-divisor graph; integers modulo ring; gaussian integer ring; Eulers’s totient function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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