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Largest Eigenvalues of Degree Sequences

Biyikoglu, Türker and Leydold, Josef (2006) Largest Eigenvalues of Degree Sequences. Research Report Series / Department of Statistics and Mathematics, 35. Department of Statistics and Mathematics, WU Vienna University of Economics and Business, Vienna.

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Abstract

We show that amongst all trees with a given degree sequence it is a ball where the vertex degrees decrease with increasing distance from its center that maximizes the spectral radius of the graph (i.e., its adjacency matrix). The resulting Perron vector is decreasing on every path starting from the center of this ball. This result it also connected to Faber-Krahn like theorems for Dirichlet matrices on trees. The above result is extended to connected graphs with given degree sequence. Here we give a necessary condition for a graph that has greatest maximum eigenvalue. Moreover, we show that the greatest maximum eigenvalue is monotone on degree sequences with respect to majorization. (author's abstract). Note: There is a more recent version of this paper available: "Graphs with Given Degree Sequence and Maximal Spectral Radius", Research Report Series / Department of Statistics and Mathematics, no. 72.

Item Type: Paper
Keywords: adjacency matrix / spectral graphthory / eigenvalues / eigenvectors / spectral radius / degree sequence / Perron vector / tree
Classification Codes: MSC_05C35, MSC_05C75, MSC_05C05, MSC_05C50
Divisions: Departments > Finance, Accounting and Statistics > Statistics and Mathematics
Depositing User: Repository Administrator
Date Deposited: 11 May 2006 13:34
Last Modified: 14 Sep 2010 19:14
URI: http://epub.wu.ac.at/id/eprint/148

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