### 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 |
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Place of Publication | Tilburg |

Publisher | Operations research |

Number of pages | 6 |

Volume | 2008-27 |

Publication status | Published - 2008 |

### Publication series

Name | CentER Discussion Paper |
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Volume | 2008-27 |

### Keywords

- Graphs
- Laplacian eigenvalues. JEL-code

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## Cite this

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.