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On the Grone-Merris conjecture

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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Tamon Stephen. On the Grone-Merris conjecture. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. pp.187-192, ⟨10.46298/dmtcs.3395⟩. ⟨hal-01184351⟩

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