Extremal Sombor Indices of Cactus Graphs‎: ‎Sparkle‎, ‎Sun‎, ‎and Broken Sun Graphs with chemical Applications

Document Type : Original paper

Authors

Department of Mathematics, Tafresh University, Tafresh 39518-79611, Iran

Abstract

In this paper‎, ‎we consider a group of cactus graphs with specific pendant edge structures such as sparkle‎, ‎sun‎, ‎and broken sun graphs‎. ‎We focus on calculating the extremal Sombor index of these graphs due to their importance in various scientific fields‎. ‎The Sombor index‎, ‎a topological index predicting physicochemical properties of molecules‎, ‎was introduced by Ivan Gutman‎. ‎This study extends previous work on Sombor indices for cactus graphs‎, ‎presenting new findings on the Sombor index of these specialized graphs and their potential use in molecular property prediction‎.

Highlights

[1] S. Alikhani and N. Ghanbari, Sombor index of polymers, MATCH Commun. Math. Comput. Chem. 86 (2021), 715–728.

[2] H. Barzegar and M. Mohammadi, Bounds for Sombor index using topological and statistical indices, J. Disc. Math. Appl. 10 (2025), no. 1, 61–85.

[3] K.C. Das, A.S. C¸evik, I.N. Cangul, and Y. Shang, On sombor index, Symmetry 13 (2021), no. 1, 140. https://doi.org/10.3390/sym13010140

[4] D. Ebbing and S.D. Gammon, General Chemistry, Cengage Learning, 2007.

[5] D.W. Green and R.H. Perry, Perry’s Chemical Engineers’ Handbook, eighth edition, McGraw Hill LLC, 2007.

[6] Hechao Liu, Lihua You, and Yufei Huang, Ordering chemical graphs by sombor indices and its applications, MATCH Commun. Math. Comput. Chem. 87 (2022), 5–22.  https://doi.org/10.46793/match.87-1.005L

[7] J. McMurry, Organic chemistry: A tenth edition, OpenStax, Rice University, 2023.

[8] J.E. McMurry, Organic Chemistry, Cengage Learning, USA, 2015.

[9] I. Milovanović, E. Milovanović, and M. Matejić, On some mathematical properties of sombor indices, Bull. Int. Math. Virtual Inst. 11 (2021), no. 2, 341–353. https://doi.org/10.7251/BIMVI2102341M

[10] M. Mohammadi, H. Barzegar, and A.R. Ashrafi, Comparisons of the Sombor index of alkane, alkyl, and annulene series with their molecular mass, J. Chem. 2022 (2022), no. 1, 8348525. https://doi.org/10.1155/2022/8348525

[11] Royal Society of Chemistry. (n.d.)., Chemspider. retrieved july 28, 2024, from http://www.chemspider.com.

[12] National Institute of Standards and Technology, Nist chemistry webbook, n.d., https://webbook.nist.gov/, Accessed: 2024-07-27.

[13] C. Phanjoubam and S.M. Mawiong, On Sombor index and some topological indices, Iranian J. Math. Chem. 12 (2021), no. 4, 209–215.

[14] H. Rezapour, R. Nasiri, and S. Mousavi, The hyper-Zagreb index of trees and unicyclic graphs, Iran. J. Math. Sci. Inform. 18 (2023), no. 1, 41–54. http://doi.org/10.52547/ijmsi.18.1.41

[15] Ž.K. Vukićević, On the Sombor index of chemical trees, Math. Montisnigri 50 (2021), 5–14. http://dx.doi.org/10.20948/mathmontis-2021-50-1

[16] S. Wagner and H. Wang, Introduction to Chemical Graph Theory, Chapman and Hall/CRC, 2018.

Keywords

Main Subjects