International Journal of Nonlinear Analysis and Applications

Sombor index of some graph operations

Document Type : Research Paper

Authors

1 Department of Mathematics, College of Computer Science and Mathematics, Tikrit University, Tikrit, Iraq

2 Mathematics Department, College of Science, University of Sulaimani, Kurdistan Region of Iraq, Iraq

3 Faculty of Ocean Engineering Technology and Informatics Universiti Malaysia Terengganu 21030, Kuala Nerus, Terengganu, Malaysia

Abstract

One of the vertex-degree based topological indices is Sombor index which is denoted by $SO(G)$, and defined by $SO(G)=\sum_{uv \in E(G)}\sqrt{d_u^2+d_v^2}$ where $d_u, d_v$ are the degree of vertices $u$ and $v$ in the graph $G$ respectively. In this paper, we are focusing on computing the Sombor index of some graph operations, more precisely join and corona product of two graphs. The original graphs that have been the base of this paper are path, cycle and complete graphs.

Keywords

[1] S. Alikhani, R. Hasni and N. E. Arif, On the atom-bond connectivity index of some families of dendrimers, J. Comput. Theor. Nanosci. 11 (2014) 1802–1805.
[2] G. Chartrand and P. Zhang, Chromatic Graph Theory, CRC press, 2019.
[3] H. Iswadi, E.T. Baskoro and R. Simanjuntak, On the metric dimension of corona product of graphs. Far East J. Math. Sci. 52 (2011) 155–170.
[4] K.C. Das, A.S. C¸ evik, I.N. Cangul and Y. Shang, On sombor index, Symmetry 13 (2021) 140.
[5] I. Gutman, Geometric approach to degree-based topological indices: Sombor indices. MATCH Commun. Math. Comput. Chem. 86 (2021) 11–16.
[6] I. Milovanovic, E. Milovanovic and M. Matejic, On some mathematical properties of sombor indices, Bull. Int. Math. Virtual Inst. 11 (2021) 341–353.
[7] I. Gutman, Some basic properties of sombor indices, Open J. Discrete Appl. Math. 4 (2021) 1–3.
[8] J. Rada, J.M. Rodr´ıguez and J.M. Sigarreta, General properties on sombor indices, Discrete Appl. Math. 299 (2021) 87-97.
[9] N. Ghanbari and S. Alikhani, Sombor index of certain graphs, arXiv preprint arXiv:2102.10409, 2021.
[10] V. Kulli, Sombor indices of certain graph operators, Int. J. Engin. Sci. Res. Technol. 10 (2021) 127–134.
[11] I. Redzepovic, Chemical applicability of sombor indices, J. Serbian Chem. Soc. 86(5) (2021) 445–457.
[12] M.N. Husin, R. Hasni, N.E. Arif and M. Imran, On topological indices of certain families of nanostar dendrimers. Molecul. 21 (2016) 821.
[13] D. Kumara, A. Mahasinghe and H. Erandi, On the abc and ga indices of the corona products of some graphs, Eurasian Chem. Commun. 3 (2021) 257-263.
International Journal of Nonlinear Analysis and Applications
Volume 13, Issue 1
March 2022
Pages 2561-2571
  • Receive Date: 02 November 2021
  • Revise Date: 30 November 2021
  • Accept Date: 09 December 2021