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

A.E. Brouwer, W.H. Haemers

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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 languageEnglish
Place of PublicationTilburg
PublisherOperations research
Number of pages6
Volume2008-27
Publication statusPublished - 2008

Publication series

NameCentER Discussion Paper
Volume2008-27

Keywords

  • Graphs
  • Laplacian eigenvalues. JEL-code

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    Brouwer, A. E., & Haemers, W. H. (2008). A Lower Bound for the Laplacian Eigenvalues of a Graph-Proof of a Conjecture by Guo. (CentER Discussion Paper; Vol. 2008-27). Operations research.