A lower bound for the Laplacian eigenvalues of a graph : Proof of a conjecture by Guo

A.E. Brouwer, W.H. Haemers

Research output: Contribution to journalArticleAcademicpeer-review

26 Citations (Scopus)

Abstract

We show that if µj is the jth largest Laplacian eigenvalue, and dj is the jth largest degree (1 = j = n) of a connected graph G on n vertices, then µj = dj - j + 2 (1 = j = n - 1). This settles a conjecture due to Guo. © 2008 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)2131-2135
JournalLinear Algebra and Its Applications
Volume429
Issue number8-9
DOIs
Publication statusPublished - 2008

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Laplacian Eigenvalues
Largest Eigenvalue
Connected graph
Lower bound
Graph in graph theory

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abstract = "We show that if µj is the jth largest Laplacian eigenvalue, and dj is the jth largest degree (1 = j = n) of a connected graph G on n vertices, then µj = dj - j + 2 (1 = j = n - 1). This settles a conjecture due to Guo. {\circledC} 2008 Elsevier Inc. All rights reserved.",
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A lower bound for the Laplacian eigenvalues of a graph : Proof of a conjecture by Guo. / Brouwer, A.E.; Haemers, W.H.

In: Linear Algebra and Its Applications, Vol. 429, No. 8-9, 2008, p. 2131-2135.

Research output: Contribution to journalArticleAcademicpeer-review

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AU - Haemers, W.H.

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AB - We show that if µj is the jth largest Laplacian eigenvalue, and dj is the jth largest degree (1 = j = n) of a connected graph G on n vertices, then µj = dj - j + 2 (1 = j = n - 1). This settles a conjecture due to Guo. © 2008 Elsevier Inc. All rights reserved.

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DO - 10.1016/j.laa.2008.06.008

M3 - Article

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JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

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