A majorization bound for the eigenvalues of some graph Laplacians
T Stephen - SIAM Journal on Discrete Mathematics, 2007 - SIAM
SIAM Journal on Discrete Mathematics, 2007•SIAM
Grone and Merris conjectured that the Laplacian spectrum of a graph is majorized by its
conjugate vertex degree sequence. In this paper, 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.
conjugate vertex degree sequence. In this paper, 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.
Grone and Merris conjectured that the Laplacian spectrum of a graph is majorized by its conjugate vertex degree sequence. In this paper, 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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