## 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)

### Stefan Felsner (ed.)

### DMTCS Conference Volume AE (2005), pp. 187-192

author: | Tamon Stephen |
---|---|

title: | On the Grone-Merris conjecture |

keywords: | graph Laplacian, majorization, graph spectrum, degree sequence |

abstract: | Grone and Merris [GM94] conjectured that the Laplacian spectrum of a graph is majorized by its conjugate vertex degree sequence. We prove that this conjecture holds for a class of graphs including trees. We also show that this conjecture and its generalization to graphs with Dirichlet boundary conditions are equivalent. |

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reference: | Tamon Stephen (2005), On the
Grone-Merris conjecture, in 2005 European Conference on
Combinatorics, Graph Theory and Applications (EuroComb
'05), Stefan Felsner (ed.), Discrete Mathematics and
Theoretical Computer Science Proceedings AE, pp.
187-192 |

bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |

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Automatically produced on Di Sep 27 10:09:52 CEST 2005 by gustedt