Sombor Index and Sombor Polynomial of the Noncommuting Graph Associated to Some Finite Groups

Authors

  • Sanhan Muhammad Salih Khasraw Department of Mathematics, College of Education, Salahaddin University-Erbil, Kurdistan Region, Iraq
  • Nor Haniza Sarmin Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor, Malaysia
  • Nur Idayu Alimon Mathematical Sciences Studies, College of Computing, Informatics and Mathematics, Universiti Teknologi MARA, Pasir Gudang Campus, 81750 Johor Bahru, Johor, Malaysia
  • Nabilah Najmuddin School of Mathematical Sciences, Universiti Sains Malaysia 11800 Gelugor, Pulau Pinang, Malaysia
  • Ghazali Semil@Ismail Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor, Malaysia

DOI:

https://doi.org/10.37934/araset.42.2.112121

Keywords:

Sombor index, Sombor polynomial, Noncommuting graph, Graph theory, Group theory

Abstract

Sombor index is a newly developed degree-based topological index which involves the degree of the vertex in a simple connected graph. The Sombor index is known as the square root of the sum of the squared degrees of two adjacent vertices in a graph. Meanwhile, the noncommuting graph associated to a group is a graph where its vertices are the non-central elements of the group and two vertices are adjacent if and only if they do not commute. In this study, a new notion called the Sombor polynomial is introduced. Then, the general formula of the Sombor index and the Sombor polynomial of the noncommuting graph associated to some finite groups are determined by using their definitions and some preliminaries. The groups involved in this research are the dihedral groups, the quasidihedral groups, and the generalized quaternion groups. The results found can help the chemists and biologists to predict the chemical and physical properties of the molecules without involving any laboratory work.

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Author Biographies

Sanhan Muhammad Salih Khasraw, Department of Mathematics, College of Education, Salahaddin University-Erbil, Kurdistan Region, Iraq

sanhan.khasraw@su.edu.krd

Nor Haniza Sarmin, Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor, Malaysia

nhs@utm.my

Nur Idayu Alimon, Mathematical Sciences Studies, College of Computing, Informatics and Mathematics, Universiti Teknologi MARA, Pasir Gudang Campus, 81750 Johor Bahru, Johor, Malaysia

idayualimon@uitm.edu.my

Nabilah Najmuddin, School of Mathematical Sciences, Universiti Sains Malaysia 11800 Gelugor, Pulau Pinang, Malaysia

nabilah.najmuddin@usm.my

Ghazali Semil@Ismail, Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor, Malaysia

ghazali85@graduate.utm.my

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Published

2024-04-03

How to Cite

Salih Khasraw, S. M., Sarmin, N. H., Alimon, N. I., Najmuddin, N., & Semil@Ismail, . G. (2024). Sombor Index and Sombor Polynomial of the Noncommuting Graph Associated to Some Finite Groups. Journal of Advanced Research in Applied Sciences and Engineering Technology, 42(2), 112–121. https://doi.org/10.37934/araset.42.2.112121

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