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

A.E. Brouwer; W.H. Haemers

doi:10.1016/j.laa.2008.06.008

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

A.E. Brouwer, W.H. Haemers

Discrete Algebra and Geometry

Research output: Contribution to journal › Article › Academic › peer-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 language	English
Pages (from-to)	2131-2135
Journal	Linear Algebra and Its Applications
Volume	429
Issue number	8-9
DOIs	https://doi.org/10.1016/j.laa.2008.06.008
Publication status	Published - 2008

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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. {\textcopyright} 2008 Elsevier Inc. All rights reserved.",

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AU - Brouwer, A.E.

AU - Haemers, W.H.

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N2 - 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.

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.

U2 - 10.1016/j.laa.2008.06.008

DO - 10.1016/j.laa.2008.06.008

M3 - Article

VL - 429

SP - 2131

EP - 2135

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

IS - 8-9

ER -