A Lower Bound for the Laplacian Eigenvalues of a Graph-Proof of a Conjecture by Guo

A.E. Brouwer; W.H. Haemers

A Lower Bound for the Laplacian Eigenvalues of a Graph-Proof of a Conjecture by Guo

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Abstract

We show that if μj is the j-th largest Laplacian eigenvalue, and dj is the j-th largest degree (1 j n) of a connected graph 蚠 on n vertices, then μj dj − j + 2 (1 j n − 1). This settles a conjecture due to Guo.

Original language	English
Place of Publication	Tilburg
Publisher	Operations research
Number of pages	6
Volume	2008-27
Publication status	Published - 2008

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Name	CentER Discussion Paper
Volume	2008-27

Keywords

Graphs
Laplacian eigenvalues. JEL-code

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2008-27

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title = "A Lower Bound for the Laplacian Eigenvalues of a Graph-Proof of a Conjecture by Guo",

abstract = "We show that if μj is the j-th largest Laplacian eigenvalue, and dj is the j-th largest degree (1 j n) of a connected graph 蚠 on n vertices, then μj dj − j + 2 (1 j n − 1). This settles a conjecture due to Guo.",

keywords = "Graphs, Laplacian eigenvalues. JEL-code",

author = "A.E. Brouwer and W.H. Haemers",

note = "Subsequently published in Linear Algebra and its Applications, 2008 Pagination: 6",

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language = "English",

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series = "CentER Discussion Paper",

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TY - UNPB

T1 - A Lower Bound for the Laplacian Eigenvalues of a Graph-Proof of a Conjecture by Guo

AU - Brouwer, A.E.

AU - Haemers, W.H.

N1 - Subsequently published in Linear Algebra and its Applications, 2008 Pagination: 6

PY - 2008

Y1 - 2008

N2 - We show that if μj is the j-th largest Laplacian eigenvalue, and dj is the j-th largest degree (1 j n) of a connected graph 蚠 on n vertices, then μj dj − j + 2 (1 j n − 1). This settles a conjecture due to Guo.

AB - We show that if μj is the j-th largest Laplacian eigenvalue, and dj is the j-th largest degree (1 j n) of a connected graph 蚠 on n vertices, then μj dj − j + 2 (1 j n − 1). This settles a conjecture due to Guo.

KW - Graphs

KW - Laplacian eigenvalues. JEL-code

M3 - Discussion paper

VL - 2008-27

T3 - CentER Discussion Paper

BT - A Lower Bound for the Laplacian Eigenvalues of a Graph-Proof of a Conjecture by Guo

PB - Operations research

CY - Tilburg

ER -

A Lower Bound for the Laplacian Eigenvalues of a Graph-Proof of a Conjecture by Guo

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