Hostname: page-component-848d4c4894-x24gv Total loading time: 0 Render date: 2024-04-30T10:48:01.933Z Has data issue: false hasContentIssue false
  • English
  • Français

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)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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