On Radenković and Gutman conjecture for some classes of trees of diameter 5

Maryam, Afeefa (Abbottabad University of Science and Technology, Pakistan)
Rahim, M. Tariq (Department of Mathematics, Abbattabad University of Science and Technology, Pakistan)
Hussain, Fawad (Department of Mathematics, Abbattabad University of Science and Technology, Pakistan)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 13, No 2 (2025): Electronic Journal of Graph Theory and Applications

The Radenković and Gutman conjecture establishes a relationship between the Laplacian energies of any tree Tn, the star graph Sn and the path graph Pn, i.e., LE(Pn) ≤ LE(Tn) ≤ LE(Sn). In this paper, we focus on verifying the validity of this conjecture for some classes of trees with diameter 5. By analyzing their structural properties and the corresponding Laplacian spectra, we establish that the conjecture holds for these few subclasses.