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arXiv · 2605.17847

Graph Theoretic and Spectral Properties of the Zero-Divisor Graph of $\mathbb{F}_p + u\mathbb{F}_p + v\mathbb{F}_p + uv\mathbb{F}_p$

N. Annamalai
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Abstract

In this article, we study the zero-divisor graph of the commutative ring with identity $R= \mathbb{F}_p + u\mathbb{F}_p + v\mathbb{F}_p + uv\mathbb{F}_p,$ where $u^2 = 0, v^2 = 0, uv = vu$ and $p$ is an odd prime. We determine several graph-theoretic properties associated with the zero-divisor graph $\Gamma(R),$ including the clique number, chromatic number, vertex connectivity, edge connectivity, diameter and girth. In addition, we compute certain topological indices of the graph $\Gamma(R).$ Furthermore, we find the eigenvalues, energy and spectral radius of the adjacency matrix, the Laplacian matrix and the Eccentricity matrix of the zero-divisor graph $(\Gamma(R).$

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N. Annamalai. 2026-05-18. Graph Theoretic and Spectral Properties of the Zero-Divisor Graph of $\mathbb{F}_p + u\mathbb{F}_p + v\mathbb{F}_p + uv\mathbb{F}_p$. https://arxiv.org/abs/2605.17847

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