Lower bound on the KG-Sombor index

Document Type : Original paper


1 Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China

2 Department of Mathematics and Computer Science, Sirjan University of Technology

3 Department of Mathematics Prince Sattam bin Abdulaziz University Alkharj 11991, Saudi Arabia


‎In 2021, a novel degree-based topological index was introduced by Gutman, called the  Sombor index. Recently Kulli and Gutman introduced a vertex-edge variant of the Sombor index, is caled KG-Sombor index. In this paper, we establish lower bound on the KG-Sombor index and determine the extremal trees achieve this bound.


Main Subjects

[1] S. Alikhani and N. Ghanbari, Sombor index of polymers, MATCH Commun. Math. Comput. Chem. 86 (2021), no. 3, 715–728.
[2] R. Cruz and J. Rada, Extremal values of the Sombor index in unicyclic and bicyclic graphs, J. Math. Chem. 59 (2021), 1098–1116.
[3] K.C. Das, A.S. Çevik, I.N. Cangul, and Y. Shang, On Sombor index, Symmetry 13 (2021), no. 1, Article ID: 140.
[4] 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.
[5] K.C. Das and Y. Shang, Some extremal graphs with respect to Sombor index, Mathematics 9 (2021), no. 11, Article ID: 1202.
[6] T. Doˇslic, Tam´as R´eti, and A. Ali, On the structure of graphs with integer Sombor indices, Discrete Math. Lett. 7 (2021), 1–4.
[7] I. Gutman, Geometric approach to degree-based topological indices: Sombor indices, MATCH Commun. Math. Comput. Chem. 86 (2021), no. 1, 11–16.
[8] I. Gutman, Some basic properties of Sombor indices, Open J. Discrete Appl. Math. 4 (2021), no. 1, 1–3.
[9] I. Gutman, N.K. Gürsoy, A. Gürsoy, and A. Ülker, New bounds on Sombor index, Commun. Comb. Optim. 8 (2023), no. 2, 305–311.
[10] I. Gutman, I. Redžepović, and V. R Kulli, KG-Sombor index of Kragujevac trees, Open J. Discrete Appl. Math. 5 (2022), no. 2, 19–25.
[11] B. Horoldagva and C. Xu, On Sombor index of graphs, MATCH Commun. Math. Comput. Chem. 86 (2021), no. 3, 703–713.
[12] V.R. Kulli, Sombor indices of certain graph operators, Int. J. Eng. Sci. Res. Tech. 10 (2021), no. 1, 127–134.
[13] V.R. Kulli, Computation of reduced Kulli-Gutman Sombor index of certain networks, J. Math. Informatics 23 (2022), 1–5.
[14] V.R. Kulli, KG Sombor indices of certain chemical drugs, Int. J. Eng. Sci. Res. Tech. 11 (2022), no. 6, 27–35.
[15] V.R. Kulli and I. Gutman, Computation of Sombor indices of certain networks, SSRG Int. J. Appl. Chem. 8 (2021), no. 1, 1–5.
[16] V.R. Kulli and I. Gutman, Sombor and KG Sombor indices of benzenoid systems and phenylenes, Ann. Pure Appl. Math. 26 (2022), no. 2, 49–53.
[17] V.R. Kulli, N. Harish, B. Chaluvaraju, and I. Gutman, Mathematical properties of KG Sombor index, Bull. Int. Math. Virt. Inst. 12 (2022), no. 2, 379–386.
[18] 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.
[19] 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.
[20] C. Phanjoubam, S.M. Mawiong, and A.M. Buhphang, On Sombor coindex of graphs, Commun. Comb. Optim. 8 (2023), no. 3, 513–529.
[21] H.S. Ramane, I. Gutman, K. Bhajantri, and D.V. Kitturmath, Sombor index of some graph transformations, Commun. Comb. Optim. 8 (2023), no. 1, 193–205.
[22] T.A. Selenge and B. Horoldagva, Extremal Kragujevac trees with respect to Sombor indices, Commun. Comb. Optim. (2023).
[23] Z. Wang, Y. Mao, Y. Li, and B. Furtula, On relations between Sombor and other degree-based indices, J. Appl. Math. Comput. 68 (2021), 1–17.