Tamon Stephen - On the Grone-Merris conjecture

dmtcs:3395 - Discrete Mathematics & Theoretical Computer Science, January 1, 2005, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05) - https://doi.org/10.46298/dmtcs.3395
On the Grone-Merris conjectureArticle

Authors: Tamon Stephen 1

  • 1 Department of Computing and Software

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.


Volume: DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Section: Proceedings
Published on: January 1, 2005
Imported on: May 10, 2017
Keywords: graph Laplacian,majorization,graph spectrum,degree sequence,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]

1 Document citing this article

Consultation statistics

This page has been seen 182 times.
This article's PDF has been downloaded 307 times.