Faber-Krahn Type Inequalities for Trees

Biyikoglu, Türker and Leydold, Josef (2003) Faber-Krahn Type Inequalities for Trees. Preprint Series / Department of Applied Statistics and Data Processing, 50. Department of Statistics and Mathematics, Abt. f. Angewandte Statistik u. Datenverarbeitung, WU Vienna University of Economics and Business, Vienna.

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Abstract

The Faber-Krahn theorem states that among all bounded domains with the same volume in Rn (with the standard Euclidean metric), a ball that has lowest first Dirichlet eigenvalue. Recently it has been shown that a similar result holds for (semi-)regular trees. In this article we show that such a theorem also hold for other classes of (not necessarily non-regular) trees. However, for these new results no couterparts in the world of the Laplace-Beltrami-operator on manifolds are known.

Item Type: Paper
Keywords: graph Laplacian / Dirichlet eigenvalue problem / Faber-Krahn type inequality / tree / degree sequence
Classification Codes: MSC 05C35, 05C75, 05C05, 05C50
Divisions: Departments > Finance, Accounting and Statistics > Statistics and Mathematics
Depositing User: Repository Administrator
Date Deposited: 10 Jul 2006 13:38
Last Modified: 22 Oct 2019 00:40
URI: https://epub.wu.ac.at/id/eprint/826

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