Spectrum of the Laplacian of an asymmetric fractal graph (2006)

Abstract: We consider a simple self-similar sequence of graphs which does not satisfy the symmetry conditions which 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 obtain a complete description of the spectra of the graphs in the sequence.