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Comb graphs and spectral decimation

Jordan, J. (2008) Comb graphs and spectral decimation. Glasgow Mathematical Journal, 51 (1). pp. 71-81. ISSN 0017-0895

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Abstract

We investigate the spectral properties of matrices associated with comb graphs. We show that the adjacency matrices and adjacency matrix Laplacians of the sequences of graphs show a spectral similarity relationship in the sense of work by L. Malozemov and A. Teplyaev (Self-similarity, operators and dynamics, Math. Phys. Anal. Geometry 6 (2003), 201–218), and hence these sequences of graphs show a spectral decimation property similar to that of the Laplacians of the Sierpiński gasket graph and other fractal graphs.

Item Type: Article
Academic Units: The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield)
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Depositing User: Mrs Megan Hobbs
Date Deposited: 22 Mar 2010 10:37
Last Modified: 07 Jun 2010 11:09
Published Version: http://dx.doi.org/10.1017/S0017089508004540
Status: Published
Publisher: Cambridge University Press
Identification Number: 10.1017/S0017089508004540
URI: http://eprints.whiterose.ac.uk/id/eprint/10612

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