The spectra of the Laplacians of fractal graphs not satisfying spectral decimation

Abstract

We consider the spectra of the Laplacians of two sequences of fractal graphs in the context of the general theory introduced by Sabot in [11]. For the sequence of graphs associated with the pentagasket, we give a description of the eigenvalues in terms of the iteration of a map from (C 2 ) 3 to itself. For the sequence of graphs introduced in [5], we show that the results found in that paper can be related to the theory in [11].