An Interlacing Approach for Bounding the Sum of Laplacian Eigenvalues of Graphs

Aida Abiad Monge; M.A. Fiol; W.H. Haemers; G. Perarnau

doi:10.1016/j.laa.2014.02.003

An Interlacing Approach for Bounding the Sum of Laplacian Eigenvalues of Graphs

Aida Abiad Monge^*, M.A. Fiol, W.H. Haemers, G. Perarnau

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

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.

Original language	English
Pages (from-to)	11-21
Journal	Linear Algebra and Its Applications
Volume	34
DOIs	https://doi.org/10.1016/j.laa.2014.02.003
Publication status	Published - 2014
Externally published	Yes

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Cite this

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title = "An Interlacing Approach for Bounding the Sum of Laplacian Eigenvalues of Graphs",

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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AU - Perarnau, G.

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AB - 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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DO - 10.1016/j.laa.2014.02.003

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JO - Linear Algebra and Its Applications

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