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The spectra of the laplacians of fractal graphs not satisfying spectral decimation

Jordan, J. (2010) The spectra of the laplacians of fractal graphs not satisfying spectral decimation. Proceedings of the Edinburgh Mathematical Society, 53 (3). pp. 731-746. ISSN 0013-0915

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Abstract

We consider the spectra of the Laplacians of two sequences of fractal graphs in the context of the general theory introduced by Sabot in 2003. For the sequence of graphs associated with the pentagasket, we give a description of the eigenvalues in terms of the iteration of a map from (C-2)(3) to itself. For the sequence of graphs introduced in a previous paper by the author, we show that the results found therein can be related to Sabot's theory.

Item Type: Article
Copyright, Publisher and Additional Information: © 2010 Cambridge University Press. This is an author produced version of a paper subsequently published in Proceeding of the Edinburgh Mathematical Society. Uploaded in accordance with the publisher's self-archiving policy.
Keywords: fractal graphs; Laplacian; spectral decimation; pentagasket
Academic Units: The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield)
Depositing User: Miss Anthea Tucker
Date Deposited: 22 Nov 2010 10:04
Last Modified: 08 Feb 2013 17:29
Published Version: http://dx.doi.org/10.1017/S0013091508000898
Status: Published
Publisher: Cambridge University Press
Refereed: Yes
Identification Number: 10.1017/S0013091508000898
URI: http://eprints.whiterose.ac.uk/id/eprint/42657

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