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

Author
Abiad, A.; Fiol, M.; Haemers, Willem H.; Perarnau-Llobet, G.
Type of activity
Journal article
Journal
Linear algebra and its applications
Date of publication
2014-05-01
Volume
448
First page
11
Last page
21
DOI
https://doi.org/10.1016/j.laa.2014.02.003 Open in new window
Project funding
Optimización y problemas extremales en teoria de grafos y combinatoria. Aplicacions a les redes de comunicación
URL
http://www.sciencedirect.com/science/article/pii/S0024379514000688 Open in new window
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 Crone, 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. (C) 2014 Elsevier Inc. All rights reserved.
Keywords
Graph spectra, Laplacian matrix, Sum of eigenvalues
Group of research
COMBGRAPH - Combinatorics, Graph Theory and Applications
GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics

Participants