Extremal unicyclic graphs with fixed leaves via Sombor index
*Saira JavedCorresponding authoraqsa.sattar@umt.edu.pkDepartment of Mathematics School of Science University of Management and TechnologyLahore, 54770, PakistanView full profile → , Aqsa Sattarjavaidmath@gmail.comDepartment of Mathematics School of Science University of Management and TechnologyLahore, 54770, PakistanView full profile → , Muhammad Javaidsaira.sheikh3434@gmail.comDepartment of Mathematics School of Science University of Management and TechnologyLahore, 54770, PakistanView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 11 Oct 2023
- Published Online:
- 18 Dec 2024
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-1988
- Pages:
- 783–795
Abstract
Keywords
Subject Classifications
References
[1] P. G. Seybold, M. May, and U. A. Bagal, “Molecular-structure property relationship,” J. Chem. Educ., vol. 64, pp. 575-581 (1987).
[2] A. T. Balaban, “Applications of graph theory in chemistry,” J. Chem. Inf. Comput. Sci., vol. 25, no. 3, pp. 334-343 (1985).
[3] A. T. Balaban, Ed., Chemical Applications of Graph Theory. London, U.K. Academic Press (1976).
[4] J. R. Dias and G. W. A. Milne, “Chemical applications of graph theory,” J. Chem. Inf. Comput. Sci., vol. 32, no. 1, pp. 210-242 (1992).
[5] P. J. Hansen and P. C. Jurs, “Chemical applications of graph theory. Part I. Fundamentals and topological indices,” J. Chem. Educ., vol. 65, pp. 574-580 (1988).
[6] H.Wiener, “Structural determination of paraffin boiling points,” J. Am. Chem. Soc., vol. 69, pp. 17-20 (1947).
[7] I. Gutman, “Degree-based topological indices,” Croat. Chem. Acta, vol. 86, pp. 351-361 (2013).
[8] D. B. West, Introduction to Graph Theory. USA: Prentice Hall (1996).
[9] I. Gutman and N. Trinajstic, “Graph theory and molecular orbitals: Total -electron energy of alternant hydrocarbons,” Chem. Phys. Lett., vol. 17, pp. 535-538 (1972).
[10] B. Furtula, A. Graovac, and D. Vukicevic, “Augmented Zagreb index,” Journal of Mathematical Chemistry, vol. 48, pp. 370-380 (2010).
[11] R. Todeschini and V. Consonni, Molecular Descriptors for Chemoinformatics: Volume I: Alphabetical Listing Volume II: Appendices, References, vol. 41. John Wiley and Sons (2009).
[12] E. Estrada, L. Torres, L. Rodriguez, and I. Gutman, “An atom-bond connectivity index: Modelling the enthalpy of formation of alkanes,” (1998).
[13] M. Ghorbani and M. A. Hosseinzadeh, “Computing ABC4 index of nanostar dendrimers,” Journal of Mathematical Chemistry, vol. 4, pp. 1419-1422, Sep. (2010).
[14] A. Ali, I. Gutman, E. Milovanovic, and I. Milovanovic, “Sum of powers of the degrees of graphs: Extremal results and bounds,” MATCH Commun. Math. Comput. Chem., vol. 80, pp. 5-84 (2018).
[15] A. Ali, L. Zhong, and I. Gutman, “Harmonic index and its generalizations: Extremal results and bounds,” MATCH Commun. Math. Comput. Chem., vol. 81, pp. 249-311 (2019).
[16] A. Sattar, M. Javaid, and M. A. Ashebo, “On the comparative analysis among topological indices for rhombus silicate and oxide structures,” Journal of Mathematics, vol. 2024, no. 1, pp. 2773913 (2024).
[17] B. Borovicanin, K. C. Das, B. Furtula, and I. Gutman, “Bounds for Zagreb indices,” MATCH Commun. Math. Comput. Chem., vol. 78, pp. 17-100 (2017).
[18] M. Javaid, A. Sattar, and E. Bonyah, “Topological aspects of molecular networks: crystal cubic carbons,” Complexity, vol. 2022, no. 1, pp. 3458094 (2022).
[19] I. Gutman, “Geometric approach to degree-based topological indices: Sombor indices,” MATCH Commun. Math. Comput. Chem., vol. 86, pp. 11-16 (2021).
[20] H. Chen, W. Li, and J. Wang, “Extremal values on the Sombor index of trees,” MATCH Commun. Math. Comput. Chem., vol. 87, pp. 87 (2022).
[21] H. Liu, “Extremal problems on Sombor indices of unicyclic graphs with a given diameter,” Comput. Appl. Math., vol. 41, no. 4, pp. 1-11 (2022).
[22] T. Zhou, Z. Lin, and L. Miao, “The extremal Sombor index of trees and unicyclic graphs with given matching number,” Journal of Discrete Mathematical Sciences and Cryptography, pp. 1-12 (2022).
[23] R. Cruz and J. Rada, “Extremal values of the Sombor index in unicyclic and bicyclic graphs,” J. Math. Chem., vol. 59, no. 4, pp. 1098-1116 (2021).
[24] M. Javaid, M. Ahmad, M. Hussain, and W. C. Teh, “Bounds of F-index for unicyclic graphs with fixed pendent vertices,” J. Prime Res. Math., vol. 14, pp. 51-61 (2018).
[25] S. Akram, M. Javaid, and M. Jamal, “Bounds on F-index of tricyclic graphs with fixed pendant vertices,” Open Mathematics, vol. 18, no. 1, pp. 150-161 (2020).
[26] R. Cruz, I. Gutman, and J. Rada, “Sombor index of chemical graphs,” Appl. Math. Comput., vol. 399, pp. 126018 (2021).
[27] H. Deng, Z. Tang, and R.Wu, “Molecular trees with extremal values of Sombor indices,” Int. J. Quantum Chem., vol. 121, pp. 26622 (2021).
[28] X. Fang, L. You, and H. Liu, “The expected values of Sombor indices in random hexagonal chains, phenylene chains and Sombor indices of some chemical graphs,” Int. J. Quantum Chem., vol. 121, pp.26740 (2021).
[29] I. Gutman, “Some basic properties of Sombor indices,” Open J. Discr. Appl. Math., vol. 4, pp. 1-3 (2021).
[30] D. Vukicevic and B. Furtula, “Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges,” J. Math. Chem., vol. 46, no. 4, pp. 1369-1376 (2009).
[31] A. Arshad, A. Sattar, M. Javaid, and M. Abebe Ashebo, “Connection number-based topological indices of Cartesian product of graphs,” Journal of Mathematics, vol. 2023, no. 1, pp. 8272936 (2023).
