A majorization bound for the eigenvalues of some graph Laplacians

Details A majorization bound for the eigenvalues of some graph Laplacians A majorization bound for the eigenvalues of some graph Laplacians

2004-11-07

arxiv.org/abs/math/0411153v1

Mathematics

Combinatorics

9 pages

Scientific paper

It is conjectured that the Laplacian spectrum of a graph is majorized by its
conjugate degree sequence. In this paper, we prove that this majorization holds
for a class of graphs including trees. We also show that a generalization of
this conjecture to graphs with Dirichlet boundary conditions is equivalent to
the original conjecture.

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