On Zero-Divisor Graph of the ring Fp+uFp+u2Fp

Document Type : Original paper

Author

Department of Basic Engineering, Lecturer in Mathematics, Government Polytechnic College, Sankarapuram, Kallakurichi-606401, Tamil Nadu, India

Abstract

In this article, we discussed the zero-divisor graph of a commutative ring with identity Fp+uFp+u2Fp 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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References

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Communications in Combinatorics and Optimization
Volume 10, Issue 1
March 2025
Pages 151-163

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