Largest Laplacian Eigenvalue and Degree Sequences of Trees

Biyikoglu, Türker and Hellmuth, Marc and Leydold, Josef (2008) Largest Laplacian Eigenvalue and Degree Sequences of Trees. Research Report Series / Department of Statistics and Mathematics, 64. Department of Statistics and Mathematics, WU Vienna University of Economics and Business, Vienna.


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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. (author´s abstract)

Item Type: Paper
Keywords: graph Laplacian / largest eigenvalue / spectral radius / eigenvector / tree / degree sequence / majorization
Classification Codes: MSC 05C35, 05C75, 05C05, 05C50
Divisions: Departments > Finance, Accounting and Statistics > Statistics and Mathematics
Depositing User: Repository Administrator
Date Deposited: 17 Apr 2008 11:04
Last Modified: 22 Oct 2019 00:41


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