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SPECTRUM OF THE LAPLACIAN OF AN ASYMMETRIC FRACTAL GRAPH

Published online by Cambridge University Press:  02 February 2006

Jonathan Jordan
Jonathan Jordan
Affiliation:
Department of Probability and Statistics, University of Sheffield, Hounsfield Road, Sheffield S3 7RH, UK (jonathan.jordan@sheffield.ac.uk)
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Abstract

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We consider a simple self-similar sequence of graphs that does not satisfy the symmetry conditions that imply the existence of a spectral decimation property for the eigenvalues of the graph Laplacians. We show that, for this particular sequence, a very similar property to spectral decimation exists, and we obtain a complete description of the spectra of the graphs in the sequence.

Keywords

Primary 28A80fractal graphLaplacianspectral decimation
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 49 , Issue 1 , February 2006 , pp. 101 - 113
Copyright
Copyright © Edinburgh Mathematical Society 2006