Energy and Spectrum of the Line Graphs of a Unit Graphs
DOI:
https://doi.org/10.11113/mjfas.v21n5.4312Keywords:
Unit graph, line graph, graph energy; graph spectrumAbstract
The study delves into an analysis of energy and spectral properties of the line graph, denoted as , derived from the unit graph offering a comprehensive mathematical exploration. Then, we begin by defining key concepts such as unit graphs, line graphs, and their spectral characteristics. Our investigation involves the computation of eigenvalues and their corresponding energy values, demonstrating how the adjacency matrix influences spectral behaviour. Furthermore, we analyse how variations in graph parameters impact energy distribution and eigenvalue structure. Theoretical derivations are supported by computational results, revealing significant trends and relationships in graph energy and spectrum. By building upon existing literature and introducing new theoretical insights, this research contributes to the ongoing development of spectral graph theory, with potential applications in network analysis, mathematical chemistry, and physics. By analysing the adjacency matrices of line graphs derived from unit graphs, this paper investigates which mean the line graphs of a unit graphs, where edges in act as vertices in , computes eigenvalues, examines graph properties, and derives general expressions for energy and spectrum. This study focuses on integer modulo rings , for specific values of .
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Copyright (c) 2025 Siti Norziahidayu Amzee Zamri, Nabilah Zulkfeli , Hazzirah Izzati Mat Hassim, Zahratul Amani Zakaria
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
