COMB GRAPHS AND SPECTRAL DECIMATION

摘要

We investigate the spectral properties ofmatrices associated with combngraphs. We show that the adjacency matrices and adjacency matrix Laplacians of thensequences of graphs show a spectral similarity relationship in the sense of work bynL.Malozemov and A. Teplyaev (Self-similarity, operators and dynamics, Math. Phys.nAnal.Geometry 6 (2003), 201–218), and hence these sequences of graphs showa spectralndecimation property similar to that of the Laplacians of the Sierpi ´ nski gasket graphnand other fractal graphs.