Largest Laplacian Eigenvalue and Degree Sequences of Trees
Combinatorics
2008-04-18 v1
Abstract
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.
Keywords
Cite
@article{arxiv.0804.2776,
title = {Largest Laplacian Eigenvalue and Degree Sequences of Trees},
author = {Tuerker Biyikoglu and Marc Hellmuth and Josef Leydold},
journal= {arXiv preprint arXiv:0804.2776},
year = {2008}
}
Comments
9 pages, 2 figures