University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 17 1 2026 03 01 Properties of Laplacian Eigenvalues of Some Bicyclic and Tricyclic Graphs 13 33 115414 10.22052/ijmc.2025.256371.1984 EN Mohammad Tariq Rahim Department of Mathematics‎, ‎Abbottabad University of Science \& Technology‎, ‎Havelian‎, ‎KPK‎, ‎Pakistan Muhammad Adnan Atta Department of Mathematics‎, ‎Abbottabad University of Science \& Technology‎, ‎Havelian‎, ‎KPK‎, ‎Pakistan Afeefa Maryam Department of Mathematics‎, ‎Abbottabad University of Science \& Technology‎, ‎Havelian‎, ‎KPK‎, ‎Pakistan Fawad Hussain Department of Mathematics‎, ‎Abbottabad University of Science \& Technology‎, ‎Havelian‎, ‎KPK‎, ‎Pakistan Journal Article 2025 03 09 ‎The Laplacian energy (LE) and the Laplacian energy-like (LEL) have recently been proposed based on molecular graph analogues of the total $\pi$-electron energy E‎. ‎Both energies have been widely studied recently because of their wide range of applications‎. ‎In the present work‎, ‎exact expressions of the Laplacian energy and the Laplacian-like invariants of bicyclic and tricyclic molecular graphs in terms of their orders have been obtained‎. ‎We also compute these expressions for the complements of these classes of graphs‎. ‎It is shown that LEL is strictly less than LE for these classes of molecular graphs‎, ‎but for their complements the inequality is the opposite‎. https://ijmc.kashanu.ac.ir/article_115414_57aa30175c23a87b502d98724acbfb12.pdf