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

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

doi:10.1016/j.laa.2014.02.003

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 journal › Article › Scientific › peer-review

4 Citations (Scopus)

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	448
DOIs	https://doi.org/10.1016/j.laa.2014.02.003
Publication status	Published - May 2014

Keywords

Laplacian matrix
graph spectra
sum of eigenvalues

Access to Document

10.1016/j.laa.2014.02.003

Cite this

@article{05fa810ae260482499e09c982b7e2f52,

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.",

keywords = "Laplacian matrix, graph spectra, sum of eigenvalues",

author = "Aida Abiad and M.A. Fiol and Haemers, {W. H.} and Guillem Perarnau",

year = "2014",

month = may,

doi = "10.1016/j.laa.2014.02.003",

language = "English",

volume = "448",

pages = "11--21",

journal = "Linear Algebra and its Applications",

issn = "0024-3795",

publisher = "Elsevier Inc.",

}

TY - JOUR

T1 - An interlacing approach for bounding the sum of Laplacian eigenvalues of graphs

AU - Abiad, Aida

AU - Fiol, M.A.

AU - Haemers, W. H.

AU - Perarnau, Guillem

PY - 2014/5

Y1 - 2014/5

N2 - 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.

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.

KW - Laplacian matrix

KW - graph spectra

KW - sum of eigenvalues

U2 - 10.1016/j.laa.2014.02.003

DO - 10.1016/j.laa.2014.02.003

M3 - Article

SN - 0024-3795

VL - 448

SP - 11

EP - 21

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

ER -

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

Abstract

Keywords

Access to Document

Fingerprint

Cite this