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

Abiad,Aida
; 
Fiol,M.A.
; 
Haemers,W. H.
; 
Perarnau,Guillem
Abstract
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.
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Date
2014-05
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Tilburg University Research Output Collection
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Keywords
Laplacian matrix, graph spectra, sum of eigenvalues
Citation
Abiad, A, Fiol, M A, Haemers, W H & Perarnau, G 2014, 'An interlacing approach for bounding the sum of Laplacian eigenvalues of graphs', Linear Algebra and its Applications, vol. 448, pp. 11-21. https://doi.org/10.1016/j.laa.2014.02.003
URI
https://hdl.handle.net/20.500.14602/69705
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