Largest Laplacian Eigenvalue and Degree Sequences of Trees

2008/04/17 by Biyikoglu, Tuerker, Hellmuth, Marc, Leydold, Josef
#05C05 #05C35 #05C50 #05C75 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.0804.2776

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.

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