Largest Laplacian Eigenvalue and Degree Sequences of Trees

Details Largest Laplacian Eigenvalue and Degree Sequences of Trees Largest Laplacian Eigenvalue and Degree Sequences of Trees

2008-04-17

arxiv.org/abs/0804.2776v1

Mathematics

Combinatorics

9 pages, 2 figures

Scientific paper

We investigate the structure of trees that have greatest maximum eigenvalue among all trees with a given degree sequence. We show that in such an extremal tree the degree sequence is non-increasing with respect to an ordering of the vertices that is obtained by breadth-first search. This structure is uniquely determined up to isomorphism. We also show that the maximum eigenvalue in such classes of trees is strictly monotone with respect to majorization.

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