GRAPH ENERGY OF THE COPRIME GRAPH ON GENERALIZED QUATERNION GROUP

  • Miftahurrahman Miftahurrahman Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Mataram, Indonesia https://orcid.org/0009-0004-0476-3598
  • I Gede Adhitya Wisnu Wardhana Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Mataram, Indonesia https://orcid.org/0000-0002-1983-1619
  • Nur Idayu Alimon College of Computing, Informatics and Mathematics, Universiti Teknologi MARA Johor, Malaysia https://orcid.org/0000-0002-3329-7897
  • Nor Haniza Sarmin Departement of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, Malaysia https://orcid.org/0000-0003-4291-5746
DOI: https://doi.org/10.30598/barekengvol20iss1pp0031-0040
Keywords: Coprime graph, Graph energy, Graph theory, Quaternion group

Abstract

This paper investigates the Degree Square Sum Energy , Degree Exponent Energy , and Degree Exponent Sum Energy  of the coprime graph on generalized quaternion group ​. This research is quantitative study using previous study as the literature review to construct the new theorem. These energy methods provide new insights into the spectral properties of graphs by their vertex degree distributions into eigenvalue computations. Using spectral graph theory, the general formulas for the , , and  of  ​ are formulated for  for every positive integer . Furthermore, we explore the implications of these methods in understanding the algebraic and spectral characteristics of  ​. Numerical results are presented for specific cases to validate the previous theorem. This study contributes to the broader analysis of graph energies, offering a framework for studying other algebraic structures.

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Published
2025-11-24
How to Cite
[1]
M. Miftahurrahman, I. G. A. Wisnu Wardhana, N. I. Alimon, and N. H. Sarmin, “GRAPH ENERGY OF THE COPRIME GRAPH ON GENERALIZED QUATERNION GROUP”, BAREKENG: J. Math. & App., vol. 20, no. 1, pp. 0031-0040, Nov. 2025.
Issue
Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Section
Articles

Copyright (c) 2025 Miftahurrahman Miftahurrahman, I Gede Adhitya Wisnu Wardhana, Nur Idayu Alimon, Nor Haniza Sarmin

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