Contents

Journal of Combinatorial Mathematics and Combinatorial Computing

  • Research article

On Radenković and Gutman Conjecture for certain Classes of Trees

Afeefa Maryam1, M. Tariq Rahim1, Fawad Hussain1
1Department of Mathematics, Abbattabad University of Science and Technology, Pakistan
  • Received: 13/09/2024
  • Accepted: 05/12/2024
  • Published: 31/12/2024

Abstract

The Radenković and Gutman conjecture establishes a relationship between the Laplacian eigenvalues of any tree \(T_n\), the star graph \(S_n\), and the path graph \(P_n\), i.e., \({LE}(P_n) \leq {LE}(T_n) \leq {LE}(S_n).\) In this paper, we prove this conjecture for a class of trees with \(n\) vertices and having diameter \(16\) to \(30\).

Keywords: Laplacian energy, Laplacian characteristics polynomial, Tree, Laplacian eigenvalues
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Citation
Afeefa Maryam, M. Tariq Rahim, Fawad Hussain. On Radenković and Gutman Conjecture for certain Classes of Trees[J], Journal of Combinatorial Mathematics and Combinatorial Computing, Volume 123. -. DOI: https://doi.org/10.61091/jcmcc123-19.