On Zero-Divisor Graph of the ring $\mathbb{F}_p+u\mathbb{F}_p+u^2 \mathbb{F}_p$

N. Annamalai

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arXiv · 2208.06004

On Zero-Divisor Graph of the ring $\mathbb{F}_p+u\mathbb{F}_p+u^2 \mathbb{F}_p$

N. Annamalai

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Abstract

In this article, we discussed the zero-divisor graph of a commutative ring with identity $\mathbb{F}_p+u\mathbb{F}_p+u^2 \mathbb{F}_p$ where $u^3=0$ 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 $\Gamma(R).$ Also, we find the eigenvalues, energy and spectral radius of both adjacency and Laplacian matrices of $\Gamma(R).$

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N. Annamalai. 2022-08-11. On Zero-Divisor Graph of the ring $\mathbb{F}_p+u\mathbb{F}_p+u^2 \mathbb{F}_p$. https://arxiv.org/abs/2208.06004

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