An interlacing approach for bounding the sum of Laplacian eigenvalues of graphs

Aida Abiad, M.A. Fiol, W. H. Haemers, Guillem Perarnau

Research output: Contribution to journalArticleScientificpeer-review


We apply eigenvalue interlacing techniques for obtaining lower and upper bounds for the sums of Laplacian eigenvalues of graphs, and characterize equality. This leads to generalizations of, and variations on theorems by Grone, and Grone & Merris. As a consequence we obtain inequalities involving bounds for some well-known parameters of a graph, such as edge-connectivity, and the isoperimetric number.
Original languageEnglish
Pages (from-to)11-21
JournalLinear Algebra and its Applications
Publication statusPublished - May 2014



  • Laplacian matrix
  • graph spectra
  • sum of eigenvalues

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