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Extended Sombor Indices | ||
Communications in Combinatorics and Optimization | ||
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 26 تیر 1404 اصل مقاله (428 K) | ||
نوع مقاله: Original paper | ||
شناسه دیجیتال (DOI): 10.22049/cco.2025.29344.1951 | ||
نویسندگان | ||
Sultan Ahmad؛ Rashid Farooq* | ||
Department of Mathematics, School of Natural Sciences, National University of Sciences and Technology, H-12, Islamabad 44000, Pakistan | ||
چکیده | ||
In this paper, we present a novel perspective on vertex-degree-based topological indices. Established degree--based topological indices are based on adjacent vertices. One could contemplate including all pairs of vertices. Recently, Gutman introduced the Sombor indices. Here, we introduce the extended versions of the Sombor indices including all pairs of vertices in the Sombor indices formula. We explore the fundamental mathematical properties of these extended indices, establish upper and lower bounds in terms of some graph parameters, and find the sharp bounds. Additionally, we determine the extremal chemical trees with maximum and minimum extended Sombor index. Moreover, the role of extended Sombor indices in describing structure–property relationships is demonstrated. | ||
کلیدواژهها | ||
Sombor indices؛ extended Sombor indices؛ chemical trees | ||
مراجع | ||
[1] S. Ahmad, R. Farooq, and K.C. Das, The general Sombor index of extremal trees with a given maximum degree, MATCH Commun. Math. Comput. Chem. 94 (2025), no. 3, 825–853. http://dx.doi.org/10.46793/match94-3.21724
[2] S. Alikhani and N. Ghanbari, Sombor index of polymers, MATCH Commun. Math. Comput. Chem. 86 (2021), no. 3, 715–728.
[3] A.R. Ashrafi, T. Došlić, and A. Hamzeh, The Zagreb coindices of graph operations, Discrete Appl. Math. 158 (2010), no. 15, 1571–1578. https://doi.org/10.1016/j.dam.2010.05.017
[4] H. Chen, W. Li, and J. Wang, Extremal values on the Sombor index of trees, MATCH Commun. Math. Comput. Chem. 87 (2022), no. 1, 23–49. https://doi.org/10.46793/match.87-1.023C
[5] R. Cruz, I. Gutman, and J. Rada, Sombor index of chemical graphs, Appl. Math. Comput. 399 (2021), Article ID: 126018. https://doi.org/10.1016/j.amc.2021.126018 [6] K.C. Das, Open problems on Sombor index of unicyclic and bicyclic graphs, Appl. Math. Comput. 473 (2024), Article ID: 128647. https://doi.org/10.1016/j.amc.2024.128647
[7] K.C. Das, A.S. Çevik, I.N. Cangul, and Y. Shang, On Sombor index, Symmetry 13 (2021), no. 1, Article ID: 140. https://doi.org/10.3390/sym13010140
[8] K.C. Das, A. Ghalavand, and A.R. Ashrafi, On a conjecture about the Sombor index of graphs, Symmetry 13 (2021), no. 10, Article ID: 1830. https://doi.org/10.3390/sym13101830
[9] K.C. Das and I. Gutman, On Sombor index of trees, Appl. Math. Comput. 412 (2022), Article ID: 126575. https://doi.org/10.1016/j.amc.2021.126575
[10] J. Devillers, No-free-lunch molecular descriptors in QSAR and QSPR, Topological Indices and Related Descriptors in QSAR and QSPR, CRC Press, 2000, pp. 11–30.
[11] B. Furtula and I. Gutman, A forgotten topological index, J. Math. Chem. 53 (2015), no. 4, 1184–1190. https://doi.org/10.1007/s10910-015-0480-z [12] R. Gozalbes, J.P. Doucet, and F. Derouin, Application of topological descriptors in QSAR and drug design: history and new trends, Curr. Drug Targets Infect. Disord. 2 (2002), no. 1, 93–102. https://doi.org/10.2174/1568005024605909
[13] I. Gutman, Selected Theorems in Chemical Graph Theory, University of Kragujevac and Faculty of Science, Kragujevac, 2017.
[14] I. Gutman, Geometric approach to degree-based topological indices: Sombor indices, MATCH Commun. Math. Comput. Chem. 86 (2021), no. 1, 11–16.
[15] I. Gutman, Some basic properties of Sombor indices, Open J. Discret. Appl. Math. 4 (2021), no. 1, 1–3. https://doi.org/10.30538/psrp–odam2021.0047
[16] I. Gutman, TEMO theorem for Sombor index, Open J. Discret. Appl. Math. 5 (2022), 25–28. https://www.doi.org/10.30538/psrp–odam2022.0067
[17] I. Gutman and N. Trinajstić, Graph theory and molecular orbitals. Total $\varphi$-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972), no. 4, 535–538. https://doi.org/10.1016/0009-2614(72)85099-1
[18] A.E. Hamza and A. Ali, On a conjecture regarding the exponential reduced Sombor index of chemical trees, Discrete Math. Lett. 9 (2022), 107–110.
[19] S. Li, Z. Wang, and M. Zhang, On the extremal Sombor index of trees with a given diameter, Appl. Math. Comput. 416 (2022), Article ID: 126731. https://doi.org/10.1016/j.amc.2021.126731
[20] X. Li and J. Zheng, Extremal chemical trees with minimum or maximum general Randi´c index, MATCH Commun. Math. Comput. Chem. 55 (2006), no. 2, 381–390.
[21] H. Liu, I. Gutman, L. You, and Y. Huang, Sombor index: review of extremal results and bounds, J. Math. Chem. 60 (2022), no. 5, 771–798. https://doi.org/10.1007/s10910-022-01333-y
[22] H. Liu, L. You, Z. Tang, and J.B. Liu, On the reduced Sombor index and its applications, MATCH Commun. Math. Comput. Chem. 86 (2021), no. 3, 729–753.
[23] J.B. Liu, X. Zhang, J. Cao, and L. Chen, Mean first-passage time and robustness of complex cellular mobile communication network, IEEE Trans. Netw. Sci. 11 (2024), no. 3, 3066–3076. https://doi.org/10.1109/TNSE.2024.3358369
[24] J.B. Liu, Y.Q. Zheng, and X.B. Peng, The statistical analysis for Sombor indices in a random polygonal chain networks, Discrete Appl. Math. 338 (2023), 218–233. https://doi.org/10.1016/j.dam.2023.06.006
[25] E. Milovanović, S. Stankov, M. Matejić, and I. Milovanović, Some observations on Sombor coindex of graphs, Commun. Combin. Optim. 9 (2024), no. 4, 813–825. https://doi.org/10.22049/cco.2023.28762.1707
[26] W. Ning, Y. Song, and K. Wang, More on Sombor index of graphs, Mathematics 10 (2022), no. 3, Article ID: 301. https://doi.org/10.3390/math10030301
[27] C. Phanjoubam, S.M. Mawiong, and A.M. Buhphang, On Sombor coindex of graphs, Commun. Combin. Optim. 8 (2023), no. 3, 513–529. https://doi.org/10.22049/cco.2022.27751.1343
[28] M. Randić, Characterization of molecular branching, J. Am. Chem. Soc. 97 (1975), no. 23, 6609–6615. https://doi.org/10.1021/ja00856a001
[29] M. Randić, Generalized molecular descriptors, J. Math. Chem. 7 (1991), no. 1, 155–168. https://doi.org/10.1007/BF01200821
[30] I. Redžepović, Chemical applicability of Sombor indices, J. Serb. Chem. Soc. 86 (2021), no. 5, 445–457. https://doi.org/10.2298/JSC201215006R
[31] Y. Shang, Sombor index and degree-related properties of simplicial networks, Appl. Math. Comput. 419 (2022), Article ID: 126881. https://doi.org/10.1016/j.amc.2021.126881
[32] M.C. Shanmukha, A. Usha, V.R. Kulli, and K.C. Shilpa, Chemical applicability and curvilinear regression models of vertex-degree-based topological index: Elliptic sombor index, Int. J. Quantum Chem. 124 (2024), no. 9, Article ID: e27376. https://doi.org/10.1002/qua.27376 [33] R. Todeschini and V. Consonni, Molecular Descriptors for Chemoinformatics: volume I: Alphabetical Listing/volume II: appendices, references, John Wiley & Sons, 2009.
[34] Z. Wang, Y. Mao, Y. Li, and B. Furtula, On relations between Sombor and other degree-based indices, J. Appl. Math. Comput. 68 (2022), no. 1, 1–17. https://doi.org/10.1007/s12190-021-01516-x
[35] C. Yang, M. Ji, K.C. Das, and Y. Mao, Extreme graphs on the Sombor indices, AIMS Math. 10 (2022), 19126–19146. http://dx.doi.org/10.3934/math.20221050
[36] B. Zhou and N. Trinajstić, On a novel connectivity index, J. Math. Chem. 46 (2009), no. 4, 1252–1270. https://doi.org/10.1007/s10910-008-9515-z | ||
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