Jordan, J. (2008) Comb graphs and spectral decimation. Glasgow Mathematical Journal, 51 (1). pp. 71-81. ISSN 0017-0895
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. Geometry 6 (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.
|Institution:||The University of Sheffield|
|Academic Units:||The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield)|
|Depositing User:||Mrs Megan Hobbs|
|Date Deposited:||22 Mar 2010 10:37|
|Last Modified:||16 Nov 2015 11:49|
|Publisher:||Cambridge University Press|