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September 26, 2025Open Access

On Spectrum of the Weakly Zero-Divisor Graph

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.

On Spectrum of the Weakly Zero-Divisor Graph

Key Points

Abstract

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