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.

https://doi.org/10.46298/dmtcs.3395
Source: HAL:hal-01184351v1
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]

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