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2 results

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

  • Part of
  • Jonathan Jordan
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 53 / Issue 3 / October 2010
    Published online by Cambridge University Press:
    12 August 2010, pp. 731-746
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  • 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.

  • SPECTRUM OF THE LAPLACIAN OF AN ASYMMETRIC FRACTAL GRAPH

  • Jonathan Jordan
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 49 / Issue 1 / February 2006
    Published online by Cambridge University Press:
    02 February 2006, pp. 101-113
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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.