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On Normalized Laplacian Spectra of the Weakly Zero-Divisor Graph of the Ring ℤ n

Author

Listed:
  • Nazim

    (Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India)

  • Nadeem Ur Rehman

    (Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India)

  • Ahmad Alghamdi

    (Mathematics Department, Faculty of Sciences, Umm Al-Qura University, P.O. Box 14035, Makkah 21955, Saudi Arabia)

Abstract

For a finite commutative ring R with identity 1 ≠ 0 , the weakly zero-divisor graph of R denoted as W Γ ( R ) is a simple undirected graph having vertex set as a set of non-zero zero-divisors of R and two distinct vertices a and b are adjacent if and only if there exist elements r ∈ ann ( a ) and s ∈ ann ( b ) satisfying the condition r s = 0 . The zero-divisor graph of a ring is a spanning sub-graph of the weakly zero-divisor graph. This article finds the normalized Laplacian spectra of the weakly zero-divisor graph W Γ ( R ) . Specifically, the investigation is carried out on the weakly zero-divisor graph W Γ ( Z n ) for various values of n .

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4310-:d:1260770
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    References listed on IDEAS

    as
    1. Yang, Xuehua & Wu, Lijiao & Zhang, Haixiang, 2023. "A space-time spectral order sinc-collocation method for the fourth-order nonlocal heat model arising in viscoelasticity," Applied Mathematics and Computation, Elsevier, vol. 457(C).
    2. 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.
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