Proceedings of the Edinburgh Mathematical Society (Series 2)

Research Article

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

Jonathan Jordana1

a1 Department of Probability and Statistics, University of Sheffield, Hounsfield Road, Sheffield S3 7RH, UK (jonathan.jordan@shef.ac.uk)

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 (ℂ2)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.

(Received September 04 2008)

Keywords

  • fractal graphs;
  • Laplacian;
  • spectral decimation;
  • pentagasket

2010 Mathematics subject classification

  • Primary 28A80