On distance Laplacian spectral ordering of some graphs

Bilal Ahmad Rather, Mustapha Aouchiche, Muhammad Imran, Issmail El Hallaoui

Research output: Contribution to journalArticlepeer-review


For a connected graph G, let DL(G) be its distance Laplacian matrix (DL matrix) and ⋌1(G)≥⋌2(G)≥⋯≥⋌n-1(G)>⋌n(G)=0 be its eigenvalues. In this article, we will study the DL spectral invariants of graphs whose complements are trees. In particular, with the technique of eigenvalue/eigenvector analysis and intermediate value theorem, we order tree complements as a decreasing sequence on the basis of their second smallest DL eigenvalue ⋌n-1, the DL spectral radius ⋌1 and the DL energy. Furthermore, we will give extreme values of ⋌1(G) and of ⋌n-1(G) over a class of unicyclic graphs and their complements. We present decreasing behaviour of these graphs in terms of ⋌1(G),⋌n-1(G) and DL energy. Thereby, we obtain complete characterization of graphs minimizing/maximizing with respect to there spectral invariants over class of these unicyclic graphs.

Original languageEnglish
Pages (from-to)867-892
Number of pages26
JournalJournal of Applied Mathematics and Computing
Issue number1
Publication statusPublished - Feb 2024


  • 05C12
  • 05C50
  • 15A18
  • Distance Laplacian energy
  • Distance Laplacian matrix
  • Double star
  • Laplacian matrix
  • Spectral invariant ordering

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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