Randic, Sum-Connectivity, and Their Product Energies of Non-Commuting Graph of Dihedral Groups

Authors

  • Mamika Ujianita Romdhini Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Mataram, Mataram 83125, Indonesia
  • Athirah Nawawi Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia
  • Faisal Al-Sharqi Department of Mathematics, Faculty of Education for Pure Sciences, University Of Anbar, Ramadi, Anbar, Iraq; Department of Mathematics, College of Education, Al-Ayen Iraqi University, An Nasiriyah, Iraq

DOI:

https://doi.org/10.19139/soic-2310-5070-4655

Keywords:

Non-commuting Graph, The Energy of a Graph, Dihedral Group, Randic Matrix, Sum-Connectivity Matrix, Product of Randic and sum-Connectivity Matrix

Abstract

One of the most extensively studied topics in chemical graph theory is graph energy. In this paper, we examine the non-commuting graph associated with the dihedral groups of order $2n$, for $n \geq 3$. We determine the spectral radius and the corresponding energies arising from the Randic, sum-connectivity, and the product of the Randic and sum-connectivity matrices of this graph. Our results show that all the obtained energies are strongly hypoenergetic. Moreover, it is shown that, in all cases, each energy is exactly equal to twice its corresponding spectral radius.

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Published

2026-09-15

How to Cite

Romdhini, M. U., Nawawi, A., & Al-Sharqi, F. (2026). Randic, Sum-Connectivity, and Their Product Energies of Non-Commuting Graph of Dihedral Groups. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-4655

Issue

Online First

Section

Research Articles

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Copyright (c) 2026 Mamika Ujianita Romdhini, Athirah Nawawi, Faisal Al-Sharqi

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