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September 26, 2025Contemporary Mathematics0 citationsOpen Access

On Spectrum of the Weakly Zero-Divisor Graph

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AKAsif Ali KhanMMMuzibur Rahman MozumderMRMohd Zamzuri Ab Rashid

Key Points

  • The study identifies the Seidel Laplacian spectrum for the weakly zero-divisor graph of finite rings, enhancing understanding of their structural properties.
  • Analysis shows distinct behaviors in the Seidel signless Laplacian spectrum across various values of n in the graph WΓ(Zn).
  • Using graph theory and properties of finite commutative rings, this work bridges algebra and combinatorial structures.
  • Implications extend to further research in algebraic structures and their associated graphical representations.

Abstract

Let us consider the finite commutative ring R, whose unity is 10. The weakly zero-divisor graph, denoted by WΓ(R), is an undirected graph whose distinct vertices c1 and c2 are adjacent if and only if, there exist r ∈ ann(c1) and s ∈ ann(c2) that satisfy the condition rs = 0. This article finds the Seidel Laplacian and Seidel signless Laplacian spectrum for the graph WΓ(Zn) for various values of n.

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Cite This Study

Khan et al. (2025) studied this question.

synapsesocial.com/papers/68d6cd5bb1249cec298b3339https://doi.org/10.37256/cm.6520258269
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