Extremal Chemical Trees for a Modified Version of Sombor Index

Document Type : Research Paper

Authors

Department of Mathematics‎, ‎Mongolian National University of Education‎, ‎Baga toiruu-14‎, ‎Ulaanbaatar‎, ‎Mongolia

Abstract

‎Let $G$ be a molecular graph, where $d_u$ representes the degree of vertex $u$‎, ‎and $uv$ denotes an edge connecting vertices $u$ and $v$‎. ‎A few years ago‎, ‎a new vertex-degree-based graph invariant (topological index) was introduced by Gutman‎, ‎defined as $SO(G)=\sum_{uv\in E}\sqrt{d_u^2+d_v^2}$‎, ‎called the Sombor index‎. ‎Recently‎, ‎Kulli et al‎. ‎compared several modified versions of Sombor index (Nirmala‎, ‎Sombor‎, ‎Dharwad‎, ‎and $F$-Sombor indices)‎, ‎they found that these indices are highly correlated and their values for QSPR applications are nearly the same‎. ‎Based on this study Kulli et al‎. introduced a new vertex-degree-based topological index‎, ‎which is defined as $X(G)=\sum_{uv\in E}\sqrt{d_u^k+d_v^k}$‎, ‎where $k\geq 1$ is a real number‎. ‎In this paper‎, ‎we determine the extremal chemical trees with respect to $X$ index‎.

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[1] I. Gutman, Geometric approach to degree–based topological indices: Sombor indices, MATCH Commun. Math. Comput. Chem. 86 (2021) 11–16.
[2] I. Damnjanovic, M. Miloševic and D. Stevanovic, A note on extremal Sombor indices of trees with a given degree sequence, MATCH Commun. Math. Comput. Chem. 90 (2023) 197–202, https://doi.org/10.46793/match.90-1.197D.
[3] S. Dorjsembe and B. Horoldagva, Reduced Sombor index of bicyclic graphs, Asian-Eur. J. Math. 15 (2022) #2250128, https://doi.org/10.1142/S1793557122501285.
[4] B. Horoldagva and C. Xu, On Sombor index of graphs, MATCH Commun. Math. Comput. Chem. 86 (2021) 703–713.
[5] H. Liu, I. Gutman, L. You and Y. Huang, Sombor index: review of extremal results and bounds, J. Math. Chem. 60 (2022) 771–798, https://doi.org/10.1007/s10910-022-01333-y.
[6] J. A. Méndez-Bermúdez, R. Aguilar–Sánchez, E. D. Molina and J. M. Rodríguez, Mean Sombor index, Discrete Math. Lett. 9 (2022) 18–25, https://doi.org/10.47443/dml.2021.s204.
[7] T. Réti, T. Došlic and A. Ali, On the Sombor index of graphs, Contrib. Math. 3 (2021) 11–18, https://doi.org/10.47443/cm.2021.0006.
[8] T. A. Selenge and B. Horoldagva, Extremal Kragujevac trees with respect to Sombor indices, Commun. Comb. Optim. 9 (2024) 177–183, https://doi.org/10.22049/CCO.2023.28058.1430.
[9] Z. Tang, Q. Li and H. Deng, Trees with extremal values of the Sombor–index–like graph invariants, MATCH Commun. Math. Comput. Chem. 90 (2023) 203–222, https://doi.org/10.46793/match.90-1.203T.

[10] A. M. Albalahi, A. Ali, Z. Du, A. A. Bhatti, T. Alraqad, N. Iqbal and A. E. Hamza, On bond incident degree indices of chemical graphs, Mathematics 11 (2023) #27, https://doi.org/10.3390/math11010027.
[11] V. R. Kulli, I. Gutman, B. Furtula and I. Redžepovic, Sombor, Nirmala, Dharwad, and F-Sombor indices - a comparative study, Int. J. Appl. Math. 10 (2023) 7–10, https://doi.org/10.14445/23939133/IJAC-V10I2P102.
[12] V. R. Kulli, Nirmala index, Int. J. Math. Trends Technol. 67 (2021) 8–12, https://doi.org/10.14445/22315373/IJMTT-V67I3P502.
[13] V. Kumar and S. Das, On Nirmala indices-based entropy measures of silicon carbide network, Iranian J. Math. Chem. 14 (2023) 271–288, https://doi.org/ 10.22052/IJMC.2023.252742.1704.
[14] V. R. Kulli, F-Sombor and modified F-Sombor indices of certain nanotubes, Ann. Pure Appl. Math. 27 (2023) 13–17, https://doi.org/10.22457/apam.v27n1a03900.

Iranian Journal of Mathematical Chemistry
Volume 15, Issue 4
December 2024
Pages 259-268

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