Exact Formulas for the Energy, Laplacian Energy, and Signless Laplacian Energy of Line Graphs of Lintang Graphs

Fransiskus Fran (Department Mathematics, Universitas Tanjungpura, Pontianak, 78124, Indonesia)
Meliana Pasaribu (Department Mathematics, Universitas Tanjungpura, Pontianak, 78124, Indonesia)
Helmi Helmi (Department Mathematics, Universitas Tanjungpura, Pontianak, 78124, Indonesia)
Raventino Raventino (Department Mathematics, Universitas Tanjungpura, Pontianak, 78124, Indonesia)

Zero : Jurnal Sains, Matematika, dan Terapan
Vol 10, No 2 (2026): Zero: Jurnal Sains Matematika dan Terapan

This study establishes exact formulas for the energy, Laplacian energy, and signless Laplacian energy of the lintang graph Ln and its line graph L(Ln). An algebraic spectral framework is employed to construct the associated matrices and determine their eigenvalues explicitly. In contrast to general results on line graph energies introduced by Ivan Gutman and subsequent studies, this work focuses on a specific two-hub graph structure for which explicit spectral formulas have not been previously reported. The results show that E(Ln) = 2 sqrt(2n), LE(L1) = QE(L1) = 10 sqrt(3), LE(Ln) = QE(Ln) = 4(n^2 - n + 2)/(n + 2) for n >= 2, and E(L(Ln)) = LE(L(Ln)) = QE(L(Ln)) = 4n - 4. These findings reveal a transition from sublinear to linear growth under the line graph transformation. The results contribute to spectral graph theory and are relevant to chemical graph theory and network analysis.