Multiplicities of distance Laplacian eigenvalues and forbidden subgraphs

Rosário Fernandes, Maria Aguieiras A. de Freitas, Celso M. da Silva, Renata R. Del-Vecchio

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


In this work, the graphs of order n having the second distance Laplacian eigenvalue of multiplicity n−2 are determined. Besides that, this result also characterizes the graphs where the multiplicity of some distance Laplacian eigenvalue is equal to n−2. In addition, all connected graphs of order n where the largest eigenvalue of the distance Laplacian matrix has multiplicity n−3 are determined. Finally, we determine some graphs with a distance Laplacian eigenvalue having multiplicity n−3.

Original languageEnglish
Pages (from-to)81-93
Number of pages13
JournalLinear Algebra and its Applications
Publication statusPublished - 15 Mar 2018


  • Distance Laplacian matrix
  • Laplacian matrix
  • Multiplicity of eigenvalues


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