On Zero-Divisor Graph of the ring \mathbbF_p+u\mathbbF_p+u² \mathbbF_p

2022/08/11 by N. Annamalai, Annamalai, N.
Mathematics · #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2208.06004

openalex publication_date 2022/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we discussed the zero-divisor graph of a commutative ring with identity \mathbbF_p+u\mathbbF_p+u² \mathbbF_p where u³=0 and p is an odd prime. We find the clique number, chromatic number, vertex connectivity, edge connectivity, diameter and girth of a zero-divisor graph associated with the ring. We find some of topological indices and the main parameters of the code derived from the incidence matrix of the zero-divisor graph Γ(R). Also, we find the eigenvalues, energy and spectral radius of both adjacency and Laplacian matrices of Γ(R).

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