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COMB GRAPHS AND SPECTRAL DECIMATION

Published online by Cambridge University Press:  01 January 2009

JONATHAN JORDAN
JONATHAN JORDAN*
Affiliation:
Department of Probability and Statistics, University of Sheffield, Hounsfield Road, Sheffield S3 7RH, UK e-mail: jonathan.jordan@shef.ac.uk
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Abstract

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We investigate the spectral properties of matrices associated with comb graphs. We show that the adjacency matrices and adjacency matrix Laplacians of the sequences of graphs show a spectral similarity relationship in the sense of work by L. Malozemov and A. Teplyaev (Self-similarity, operators and dynamics, Math. Phys. Anal. Geometry6 (2003), 201–218), and hence these sequences of graphs show a spectral decimation property similar to that of the Laplacians of the Sierpiński gasket graph and other fractal graphs.

Keywords

Primary 47A10Secondary 05C9928A80
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 51 , Issue 1 , January 2009 , pp. 71 - 81
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

References

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