Comb graphs and spectral decimation (2009)
Glasgow Mathematical Journal, vol. 51, pp. 71-81.
Abstract: 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 Malozemov and Teplyaev, and hence that these sequences graphs show a spectral decimation property similar to that of the Laplacians of the Sierpiński gasket graph and other fractal graphs.
AMS 2000 subject classification: Primary 47A10, secondary 05C99, 28A80.