Largest Laplacian Eigenvalue and Degree Sequences of Trees

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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.
9 pages, 2 figures

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Combinatorics, 05C35; 05C75; 05C05; 05C50

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http://salesiana.dossiersoluciones.com/handle/123456789/159042

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0804.2776
 http://arxiv.org/abs/0804.2776

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arXiv