Abstract
We apply interlacing techniques for obtaining lower and upper bounds for the sums of Laplacian eigenvalues of graphs. Mainly, we generalize two theorems of Grone and Grone & Merris, providing tight bounds and studying the cases of equality. As a consequence, some results on well-known parameters of a graph, such as the maximum and minimum cuts, the edge-connectivity, the (almost) dominating number, and the edge isoperimetric number, are derived.
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© 2013 Scuola Normale Superiore Pisa
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Abiad, A., Fiol, M.A., Haemers, W.H., Perarnau, G. (2013). An interlacing approach for bounding the sum of Laplacian eigenvalues of graphs. In: Nešetřil, J., Pellegrini, M. (eds) The Seventh European Conference on Combinatorics, Graph Theory and Applications. CRM Series, vol 16. Edizioni della Normale, Pisa. https://doi.org/10.1007/978-88-7642-475-5_18
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DOI: https://doi.org/10.1007/978-88-7642-475-5_18
Publisher Name: Edizioni della Normale, Pisa
Print ISBN: 978-88-7642-474-8
Online ISBN: 978-88-7642-475-5
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