On Sombor coindex of graphs

Document Type : Original paper


1 Mathematics Department, North Eastern Hill University Shillong India

2 Department of Basic Sciences and Social Sciences, North Eastern Hill University, Mawlai Umshing, Shillong, Meghalaya, India Pin code - 793022

3 Department of Mathematics, North Eastern Hill University Shillong India


In this paper, we explore several properties of Sombor coindex of a finite simple graph and we derive a bound for the total Sombor index. We also explore its relations to the Sombor index, the Zagreb coindices, forgotten coindex and other important graph parameters. We further compute the bounds of the Somber coindex of some graph operations and derived explicit formulae of Sombor coindex for some well-known graphs as application.


Main Subjects

[1] A.R. Ashrafi, T. Došlić, and A. Hamzeh, The Zagreb coindices of graph operations, Discrete Appl. Math. 158 (2010), no. 15, 1571–1578.
[2] M. Azari and F. Falahati-Nezhed, Some results on forgotten topological coindex, Iranian J. Math. Chem. 10 (2019), no. 4, 307–318.
[3] R. Cruz, I. Gutman, and J. Rada, Sombor index of chemical graphs, Appl. Math. Comput. 399 (2021), ID: 126018.
[4] K.C. Das, A.S. Çevik, I.N. Cangul, and Y. Shang, On sombor index, Symmetry 13 (2021), no. 1, ID: 140.
[5] N. De, S. Nayeem, M. Abu, and A. Pal, The F-coindex of some graph operations, Springer Plus 5 (2016), no. 1, Art: 221.
[6] T. Došlić, Vertex-weighted Wiener polynomials for composite graphs, Ars Math. Contemp. 1 (2008), no. 1, 66–80.
[7] S.S. Dragomir, A survey on Cauchy-Bunyakovsky-Schwarz type discrete inequalities, J. Inequal. Pure Appl. Math. 4 (2003), no. 3, Art. 63.
[8] S. Filipovski, Relations between Sombor index and some degree-based topological
indices, Iranian J. Math. Chem. 12 (2021), no. 1, 19–26.
[9] I. Gutman, Geometric approach to degree-based topological indices: Sombor indices, MATCH Commun. Math. Comput. Chem. 86 (2021), no. 1, 11–16.
[10] I. Gutman, N.K. Gürsoy, A. Gürsoy, and A. Ülker, New bounds on sombor index, Commun. Comb. Optim. (In press).
[11] D.J. Klein, T. Došlić, and D. Bonchev, Vertex-weightings for distance moments and thorny graphs, Discrete Appl. Math. 155 (2007), no. 17, 2294–2302.
[12] X. Li and J. Zheng, A unified approach to the extremal trees for different indices, MATCH Commun. Math. Comput. Chem. 54 (2005), no. 1, 195–208.
[13] I. Milovanović, M. Matejić, E. Milovanović, and R. Khoeilar, A note on the first Zagreb index and coindex of graphs, Commun. Comb. Optim. 6 (2021), no. 1, 41–51.
[14] C. Phanjoubam and S.Mn. Mawiong, On Sombor index and some topological indices, Iranian J. Math. Chem. 12 (2021), no. 4, 209–215.
[15] H.S. Ramane, I. Gutman, K. Bhajantri, and D.V. Kitturmath, Sombor index of some graph transformations, Commun. Comb. Optim. (In press).
[16] I. Redžepović, Chemical applicability of Sombor indices, J. Serb. Chem. Soc. 86 (2021), no. 5, 445–457.
[17] T. Réti, T. Došlić, and A. Ali, On the sombor index of graphs, Contrib. Math. 3 (2021), 11–18.
[18] N.H.A.M. Saidi, M.N. Husin, and N.B. Ismail, Zagreb indices and Zagreb coindices of the line graphs of the subdivision graphs, J. Discrete Math. Sci. Cryptogr. 23 (2020), no. 6, 1253–1267.
[19] 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.
[20] H. Wiener, Structural determination of paraffin boiling points, J. Am. Chem. Soc. 69 (1947), no. 1, 17–20.