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

Author

Listed:
  • 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)

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

Suggested Citation

  • Bilal A. Rather & Shariefuddin Pirzada & Tariq A. Naikoo & Yilun Shang, 2021. "On Laplacian Eigenvalues of the Zero-Divisor Graph Associated to the Ring of Integers Modulo n," Mathematics, MDPI, vol. 9(5), pages 1-17, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:482-:d:506347
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    References listed on IDEAS

    as
    1. Abdollah Alhevaz & Maryam Baghipur & Kinkar Ch. Das & Yilun Shang, 2020. "Sharp Bounds on (Generalized) Distance Energy of Graphs," Mathematics, MDPI, vol. 8(3), pages 1-20, March.
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    Cited by:

    1. Nazim & Nadeem Ur Rehman & Ahmad Alghamdi, 2023. "On Normalized Laplacian Spectra of the Weakly Zero-Divisor Graph of the Ring ℤ n," Mathematics, MDPI, vol. 11(20), pages 1-14, October.

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