On Zero-Divisor Graph of the ring 𝔽_p+u𝔽_p+u^2 𝔽_p

08/11/2022

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by   N. Annamalai, et al.

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In this article, we discussed the zero-divisor graph of a commutative ring with identity 𝔽_p+u𝔽_p+u^2 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 Γ(R). Also, we find the eigenvalues, energy and spectral radius of both adjacency and Laplacian matrices of Γ(R).