Sombor index of Kragujevac trees

Authors: Gutman Ivan, Kulli Veerabhadrappa R., Redžepović Izudin

Keywords: Sombor index; Kragujevac tree; Zagreb index

Abstract:

The paper is concerned with the Sombor index (SO) of Kragujevac trees (Kg). A slightly more general definition of Kg is offered. SO is a recently introduced degree-based topological index. A general combinatorial expression for SO(Kg) is established. The species with minimum and maximum SO(Kg)-values are determined.

References:

[1]Ali, A., Das, K.C., Dimitrov, D., Furtula, B. (2021) Atom-bond connectivity index of graphs: a review over extremal results and bounds. Discrete Mathematics Letters, 5: 68-93 [2]Alikhani, S., Ghanbari, N. (2021) Sombor index of polymers. MATCH Commun. Math. Comput. Chem, 86: 715-728 [3]Basavanagoud, B., Timmanaikar, S. (2017) Computing first Zagreb and forgotten indices of certain dominating transformation graphs of Kragujevac trees. J. Comput. Math. Sci, 8(3): 50-61 [4]Bondy, J.A., Murty, U.S.R. (1976) Graph Theory with Applications. New York: Macmillan Press [5]Cruz, R., Gutman, I., Rada, J. (2014) Topological indices of Kragujevac trees. Proyecciones J. Math, 33: 471-482 [6]Cruz, R., Rada, J. (2021) Extremal values of the Sombor index in unicyclic and bicyclic graphs. Journal of Mathematical Chemistry, 59: 1098-1116 [7]Das, K.C., Evik, A.S.C., Cangul, I.N., Shang, Y. (2021) On Sombor Index. Symmetry, 13: 140 [8]Deng, H., Tang, Z., Wu, R. (2021) Molecular trees with extremal values of Sombor indices. Int. J. Quantum Chem, 121(11): e26622 [9]Dimitrov, D. (2014) On structural properties of trees with minimal atom-bond connectivity index. Discr. Appl. Math, 172: 28-44 [10]Gutman, I. (2021) Geometric approach to degree-based topological indices: Sombor indices. MATCH Commun. Math. Comput. Chem, 86: 11-16 [11]Gutman, I., Trinajstić, N. (1972) Graph theory and molecular orbitals. Total ph-electron energy of alternant hydrocarbons. Chemical Physics Letters, 17: 535-538 [12]Gutman, I. (2014) Kragujevac trees and their energy. Scientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informatics and mechanics, vol. 6, br. 2, str. 71-79 [13]Gutman, I. (2021) Some basic properties of Sombor indices. Open Journal of Discrete Applied Mathematics, 4(1): 1-3 [14]Hosseini, S.A., Ahmadi, M.B., Gutman, I. (2014) Kragujevac trees with minimal atom-bond connectivity index. MATCH Commun. Math. Comput. Chem, 71: 5-20 [15]Kulli, V.R. (2012) College Graph Theory. Gulbarga: Vishwa International Publications [16]Kulli, V.R. (2021) Sombor index of certain graph operators. Int. J. Eng. Sci. Res. Technol, 10: 127-134 [17]Milovanović, I., Milovanović, E., Mateji’c, M. (2021) On some mathematical properties of Sombor indices. Bull. Internat. Math. Virt. Inst, 11: 341-353 [18]Mirajkar, K.G., Doddamani, B.R., Priyanka, Y.B. (2017) Atom bond connectivity indices of Kragujevac trees. International Journal of Current Research and Review, 9(15): 1-7 [19]Rada, J., Rodriguez, J.M., Sigarreta, J.M. (2021) General properties on Sombor indices. Discr. Appl. Math., 299: 87-97 [20]Redžepović, I. (2021) Chemical applicability of Sombor indices. Journal of the Serbian Chemical Society, 86: 000-000 [21]Rezaei, M., Hosamani, S.M., Farahani, M.R., Jamil, M.K. (2017) On the terminal Wiener index and Zagreb indices of Kragujevac trees. Int. J. Pure Appl. Math, 113: 617-625 [22]Shirkol, S.S., Hosamani, S.M., Patil, S.V. (2017) Acharya polynomial of some graph transformations. Bull. Math. Statist. Res, 5: 75-83 [23]Wagner, S., Wang, H. (2018) Introduction to Chemical Graph Theory. Boca Raton: CRC Press