On Sombor Energy of the Nilpotent Graph of the Ring of Integers Modulo ε
Abstract
In chemical graph theory, chemical compounds are represented as graphs where atoms are represented as vertices, and the bonds connecting the atoms are represented as edges. In 2021, Gowtham and Swamy discovered another type of graph energy, called the Sombor energy. This discovery was motivated by Gutman's introduction of the Sombor index in the same year. In the field of abstract algebra, rings can also be represented as graphs. In this article, we aim to explore the Sombor energy of some nilpotent graphs of rings, particularly the ring of integers modulo ε.
Full text article
References
R. Garc´ıa-Domenech, J. G´alvez, J. V. de Juli´an-Ortiz, and L. Pogliani, “Some new trendsin chemical graph theory,” Chemical Reviews, vol. 108, no. 3, pp. 1127–1169, 2008. https://doi.org/10.1021/cr0780006.
N. Nurhabibah, I. G. A. W. Wardhana, and N. W. Switrayni, “Numerical invariants of coprime graph of a generalized quaternion group,” Journal of the Indonesian Mathematical Society, pp. 36–44, 2023. https://doi.org/10.22342/jims.29.1.1245.36-44.
M. Afdhaluzzikri, I. G. A. W. Wardhana, F. Maulana, and H. R. Biswas, “The non-coprime graphs of upper unitriangular matrix groups over the ring of integer modulo with prime order and their topological indices,” BAREKENG: Jurnal Ilmu Matematika dan Terapan, vol. 19, no. 1, pp. 547–556, 2025. https://doi.org/10.30598/barekengvol19iss1pp547-556.
S. Zahidah, D. M. Mahanani, and K. L. Oktaviana, “Connectivity indices of coprime graph of generalized quaternion group,” J. Indones. Math. Soc, vol. 27, no. 3, pp. 285–296, 2021. https://doi.org/10.22342/jims.27.3.1043.285-296.
J. Yang, M. H. Muhammad, M. K. Siddiqui, M. F. Hanif, M. Nasir, S. Ali, and J.-B. Liu, “Topological co-indices of hydroxyethyl starch conjugated with hydroxychloroquine used for covid-19 treatment,” Polycyclic Aromatic Compounds, vol. 42, no. 10, pp. 7130–7142, 2022. https://doi.org/10.1080/10406638.2021.1996407.
Gutman and I, “The energy of graph,” Ber. Math.Stat. Sekt. Forschungszent. Graz, pp. 1–22, 1978.
R. Balakrishnan, “The energy of a graph,” Linear Algebra and its Applications, vol. 387, pp. 287–295, 2004. https://doi.org/10.1016/j.laa.2004.02.038.
G. Y. Karang, I. G. A. W. Wardhana, N. I. Alimon, and N. H. Sarmin, “Energy and degree sum energy of non-coprime graphs on dihedral groups,” Journal of the Indonesian Mathematical Society, vol. 31, no. 1, pp. 1900–1900, 2025. https://doi.org/10.22342/jims.v31i1.1900.
D. P. Malik, M. N. Husni, M. Miftahurrahman, I. G. A. W. Wardhana, G. Semil, et al., “the chemical topological graph associated with the nilpotent graph of a modulo ring of prime power order,” Journal of Fundamental Mathematics and Applications (JFMA), vol. 7, no. 1, pp. 1–9, 2024. https://doi.org/10.14710/jfma.v0i0.20269.
K. J. Gowtham and S. N. Narasimha, “On sombor energy of graphs,” Наносистемы: физика, химия, математика, vol. 12, no. 4, pp. 411–417, 2021. https://doi.org/10.17586/2220-8054-2021-12-4-411-417.
I. Gutman, I. Redˇzepovi´c, and J. Rada, “Relating energy and sombor energy,” Contrib. Math, vol. 4, pp. 41–44, 2021. https://doi.org/10.47443/cm.2021.0054.
H. S. Ramane and S. S. Shinde, “Degree exponent polynomial of graphs obtained by some graph operations,” Electronic Notes in Discrete Mathematics, vol. 63, pp. 161–168, 2017. https://doi.org/10.1016/j.endm.2017.11.010.
Authors
Copyright (c) 2025 Journal of the Indonesian Mathematical Society
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Article Details
