Bounds on the Energy of Zero-divisor Graph of Quotient Ring and Its Topological Indices

Authors

  • Vira Hari Krisnawati Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang, East Java, Indonesia https://orcid.org/0000-0003-2666-9231
  • Noor Hidayat Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang, East Java, Indonesia
  • Ayunda Faizatul Musyarrofah Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang, East Java, Indonesia

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i2.5971

Keywords:

zero-divisor graph, graph energy, distance-based topological indices, degree-based topological indices

Abstract

In this paper, we study the zero-divisor graph of \( \mathbb{Z}_{\powerset}[x]/\langle x^5 \rangle \) for prime number \( \powerset \), denoted as \(\Gamma(\mathbb{Z}_{\powerset}[x]/\langle x^5 \rangle) \), including its energy and topological indices. Specifically, we provide bounds of the energy for \(\Gamma(\mathbb{Z}_{\powerset}[x]/\langle x^5 \rangle) \) and show that these bounds are numerically close to the actual energy value. Furthermore, we determine the topological indices of \(\Gamma(\mathbb{Z}_{\powerset}[x]/\langle x^5 \rangle) \), including the topological indices based on distance and degree. We also perform numerical simulations of the topological indices for various prime numbers \( \powerset \).

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Published

2025-05-01

Issue

Vol. 18 No. 2: (April 2025)

Section

Algebra

License

Copyright (c) 2025 Vira Hari Krisnawati, Noor Hidayat, Ayunda Faizatul Musyarrofah

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How to Cite

Bounds on the Energy of Zero-divisor Graph of Quotient Ring and Its Topological Indices. (2025). European Journal of Pure and Applied Mathematics, 18(2), 5971. https://doi.org/10.29020/nybg.ejpam.v18i2.5971