Properties of Laplacian Eigenvalues of Some Bicyclic and Tricyclic Graphs
نویسندگان
1 Department of Mathematics, Abbottabad University of Science \& Technology, Havelian, KPK, Pakistan
2 Department of Mathematics, Abbottabad University of Science \& Technology, Havelian, KPK, Pakistan
3 Department of Mathematics, Abbottabad University of Science \& Technology, Havelian, KPK, Pakistan
4 Department of Mathematics, Abbottabad University of Science \& Technology, Havelian, KPK, Pakistan
doi
10.22052/ijmc.2025.256371.1984چکیده
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.
