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On Zero-Divisor Graph of the ring $\mathbb{F}_p+u\mathbb{F}_p+u^2 \mathbb{F}_p$ | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 9، دوره 10، شماره 1، خرداد 2025، صفحه 151-163 اصل مقاله (414.71 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2023.28238.1486 | ||
| نویسنده | ||
| N. Annamalai* | ||
| Department of Basic Engineering, Lecturer in Mathematics, Government Polytechnic College, Sankarapuram, Kallakurichi-606401, Tamil Nadu, India | ||
| چکیده | ||
| 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 $\Gamma(R).$ | ||
| کلیدواژهها | ||
| zero-divisor graph؛ Laplacian matrix؛ spectral radius | ||
| مراجع | ||
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