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Sombor, Nirmala, Dharwad, and F-Sombor Indices – A Comparative Study

International Journal of Applied Chemistry
© 2023 by SSRG - IJAC Journal
Volume 10 Issue 2
Year of Publication : 2023
Authors : V. R. Kulli, I.Gutman, B. Furtula, I. Redzepovic
10.14445/23939133/IJAC-V10I2P102
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How to Cite?

V. R. Kulli, I.Gutman, B. Furtula, I. Redzepovic, "Sombor, Nirmala, Dharwad, and F-Sombor Indices – A Comparative Study," SSRG International Journal of Applied Chemistry, vol. 10,  no. 2, pp. 7-10, 2023. Crossref, https://doi.org/10.14445/23939133/IJAC-V10I2P102

Abstract:

Let G be a molecular graph, d(u) the degree (number of first neighbors) of its vertex u, and uv its edge connecting the vertices u and v. In the recent literature, four vertex-degree-based molecular structure descriptors have been put forward, named Nirmala, Sombor, Dharwad, and F-Sombor indices, equal to the sum of the terms √d(u)k + d(v) k over all edges uv of G for k=1,2,3, and 4. In this work, we compare these four indices. We find that they are highly correlated, and their value for QSPR applications is nearly the same. Therefore, only one (any one) of these topological indices should be used. From an applicative point of view, there was no need to introduce and study them separately.

Keywords:

Sombor index, Nirmala index, Dharwad index, F-Sombor index, QSPR studies.

References:

[1] Alexandru Balaban, Chemical Applications of Graph Theory, Academic Press, London, 1976.
[Google Scholar] [Publisher Link]
[2] Nenad Trinajstic, Chemical Graph Theory, 2nd Edition, CRC Press, Boca Raton, 1983.
[CrossRef] [Google Scholar] [Publisher Link]
[3] Ivan Gutman, and Oskar E. Polansky, Mathematical Concepts in Organic Chemistry, Springer, Berlin, 1986.
[CrossRef] [Google Scholar] [Publisher Link]
[4] Stephan Wagner, and Hua Wang, Introduction to Chemical Graph Theory, CRC Press, Boca Raton, 2018.
[Google Scholar] [Publisher Link]
[5] James Devillers, and Alexandru T Balaban, Topological Indices and Related Descriptors in QSAR and QSPR, Gordon and Breach, Amsterdam, 1999.
[Google Scholar] [Publisher Link]
[6] Mati Karelson, Molecular Descriptors in QSAR/QSPR, Wiley, New York, 2000.
[Google Scholar] [Publisher Link]
[7] Tomasz Puzyn, Jerzy Leszczynski, and Mark T. Cronin, Recent Advances in QSAR Studies-Methods and Applications, Springer, Dordrecht, 2010.
[Google Scholar] [Publisher Link]
[8] Roberto Todeschini, and Viviana Consonni, Molecular Descriptors for Chemoinformatics, Wiley-VCH, Weinheim 2009.
[CrossRef] [Google Scholar] [Publisher Link]
[9] Madhumangal Pal, Sovan Samanta, and Anita Pal, Handbook of Research of Advanced Applications of Graph Theory in Modern Society, Global, Hershey, pp. 66-91, 2020.
[CrossRef] [Google Scholar] [Publisher Link]
[10] Ivan Gutman, “Geometric Approach to Degree-Based Topological Indices: Sombor Indices,” MATCH Communications in Mathematical and in Computer Chemistry, vol. 86, pp. 11-16, 2021.
[Google Scholar] [Publisher Link]
[11] Saeid Alikhani, and Nima Ghanbari, “Sombor Index of Polymers,” MATCH Communications in Mathematical and in Computer Chemistry, vol. 86, pp. 715-728, 2021.
[Google Scholar] [Publisher Link]
[12] Gowtham K.J, “Entropy Measures of Some Nanotubes Using Sombor Index,” NanoNEXT, vol. 3, no. 3, pp. 1-5, 2022.
[CrossRef] [Google Scholar] [Publisher Link]
[13] V.R. Kulli, “Sombor Indices of Two Families of Dendrimer Nanostars,” Annals of Pure and Applied Mathematics, vol. 24, no. 1, pp. 21-26, 2021.
[CrossRef] [Google Scholar] [Publisher Link]
[14] Hechao Liu et al., “More on Sombor Indices of Chemical Graphs and Their Applications to the Boiling Point of Benzenoid Hydrocarbons,” International Journal of Quantum Chemistry, vol. 121, no. 17, 2021.
[CrossRef] [Google Scholar] [Publisher Link]
[15] Maryam Mohammadi, Hasan Barzegar, and Ali Reza Ashrafi, “Comparisons of the Sombor Index of Alkane, Alkyl, and Annulene Series with Their Molecular Mass,” Journal of Chemistry, 2022.
[CrossRef] [Google Scholar] [Publisher Link]
[16] Fateme Movahedi, and Mohammad Hadi Akhbari, “Degree-Based Topological Indices of the Molecular Structure of Hyaluronic Acid-Methotrexate Conjugates in Cancer Treatment,” International Journal of Quantum Chemistry, vol. 123, no. 7, 2023.
[CrossRef] [Google Scholar] [Publisher Link]
[17] Izudin Redžepović, “Chemical Applicability of Sombor Indices,” Journal of the Serbian Chemical Society, vol. 86, no. 5, pp. 445- 457, 2021.
[CrossRef] [Google Scholar] [Publisher Link]
[18] Muhammad Shoaib Sardar et al., “Computation of Sombor Indices for Some Classes of Silicon Carbides,” Mathematical Statistician and Engineering Applications, vol. 71, no. 3, pp. 81-97, 2022.
[CrossRef] [Google Scholar] [Publisher Link]
[19] Ashwini Ankanahalli Shashidhara et al., “Domination Version: Sombor Index of Graphs and its Significance in Predicting Physicochemical Properties of Butane Derivatives,” Eurasian Chemical Communications, vol. 5, pp. 91-102, 2023.
[CrossRef] [Google Scholar] [Publisher Link]
[20] Hechao Liu et al., “Sombor Index: Review of Extremal Results and Bounds,” Journal of Mathematical Chemistry, vol. 66, pp. 771- 798, 2022.
[CrossRef] [Google Scholar] [Publisher Link]
[21] V.R. Kulli, “Nirmala Index,” International Journal of Mathematics Trends and Technology, vol. 67, no. 3, pp. 8-12, 2021.
[CrossRef] [Google Scholar] [Publisher Link]
[22] V.R. Kulli, “Dharwad Index,” International Journal of Engineering Sciences and Research Technology, vol. 10, no. 4, pp. 17-21, 2021.
[CrossRef] [Publisher Link]
[23] V.R. Kulli, “F-Sombor and Modified F-Sombor Indices of Certain Nanotubes,” Annals of Pure and Applied Mathematics, vol. 27, no. 1, pp. 13-17, 2023.
[CrossRef] [Google Scholar] [Publisher Link]
[24] Ivan Gutman, “Some Basic Properties of Sombor Indices,” Open Journal of Discrete Applied Mathematics, vol. 4, no. 1, pp. 1-3, 2021.
[CrossRef] [Google Scholar] [Publisher Link]
[25] V.R. Kulli, and Ivan Gutman, “On Some Mathematical Properties of Nirmala Index,” Annals of Pure and Applied Mathematics, vol. 23, pp. 93-99, 2021.
[CrossRef] [Google Scholar] [Publisher Link]
[26] Roberto Cruz, and Juan Rada, “The Path and the Star as Extremal Values of Vertex-Degree-Based Topological Indices among Trees,” MATCH Communications in Mathematical and in Computer Chemistry, vol. 82, pp. 715-732, 2019.
[Google Scholar] [Publisher Link]
[27] Ivan Gutman, and Kinkar Ch. Das, “The First Zagreb Index 30 Years After,” MATCH Communications in Mathematical and in Computer Chemistry, vol. 50, pp. 83-92, 2004.
[Google Scholar] [Publisher Link]
[28] Boris Furtula, and Ivan Gutman, “A Forgotten Topological Index,” Journal of Mathematical Chemistry, vol. 53, pp. 1184-1190, 2015.
[CrossRef] [Google Scholar] [Publisher Link]