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Abdurahim
Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Mataram, Mataram, 83125, Indonesia
Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Environmental Science Materials Science & Nanotechnology Physics

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Zagreb-Based Indices of Line Graph of Prime Coprime Graph for Integers Modulo Group Abdurahim; Mamika Ujianita Romdhini; Jihadil Qudsi
Science and Technology Indonesia Vol. 11 No. 3 (2026): July
Publisher : Research Center of Inorganic Materials and Coordination Complexes, FMIPA Universitas Sriwijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26554/sti.2026.11.3.844-854

Abstract

In this paper, we investigate the line graph of the prime coprime graph associated with the integers modulo group. Explicit general formulas are derived for the first Zagreb index, the second Zagreb index, and the hyper-Zagreb index of the considered structures. A comparative analysis is performed between the newly obtained results and previously reported findings, highlighting structural differences and index growth behaviour under the line-graph transformation. Furthermore, a statistical analysis is conducted to explore the quantitative relationship between the prime coprime graph and its corresponding line graph with respect to the computed Zagreb-based indices. The results provide deeper insight into the structural complexity of algebraically defined graphs and clarify how degree-based topological descriptors evolve under graph transformations.
On the Spectral Characterization of Prime Coprime Graphs Associated with Dihedral Groups Mamika Ujianita Romdhini; Abdurahim; Adem Kilicman; Dragan Pamucar; Faisal Al-Sharqi; Ifan Hasnan Dani; Marliadi Susanto
Science and Technology Indonesia Vol. 11 No. 4 (2026): October
Publisher : Research Center of Inorganic Materials and Coordination Complexes, FMIPA Universitas Sriwijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26554/sti.2026.11.4.1516-1523

Abstract

Spectral graph theory and group theory help reveal how the structure of graphs shapes their mathematical properties. This research aims to analyze the spectral descriptors of the prime coprime graph of a dihedral group associated with the Laplacian, normalized Laplacian, and Seidel matrices. We also establish a method for determining the eigenvalues of these matrices. The results show that the Laplacian, signless Laplacian, and normalized Laplacian energies of the obtained graph are always even integers, whereas the adjacency and Seidel energies are never odd integers. These findings are consistent with previous studies and further strengthen the role of spectral descriptors in understanding algebraicgraph structures.
Co-Authors Adem Kilicman Dragan Pamucar Faisal Al-Sharqi Ifan Hasnan Dani Jihadil Qudsi Mamika Ujianita Romdhini Mamika Ujianita Romdhini Marliadi Susanto