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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Maryam, Afeefa
Abbottabad University of Science and Technology, Pakistan
Electrical & Electronics Engineering

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On Radenković and Gutman conjecture for some classes of trees of diameter 5 Maryam, Afeefa; Rahim, M. Tariq; Hussain, Fawad
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 13, No 2 (2025): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2025.13.2.4

Abstract

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.
Co-Authors Hussain, Fawad Rahim, M. Tariq