@TECHREPORT{Krön01growthof, author = {B. Krön}, title = {Growth of self-similar graphs}, institution = {}, year = {2001} }

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Abstract

Abstract. Locally finite self-similar graphs with bounded geometry and without bounded geometry as well as non-locally finite self-similar graphs are characterized by the structure of their cell graphs. Geometric properties concerning the volume growth and distances in cell graphs are discussed. The length scaling factor ν and the volume scaling factor µ can be defined similarly to the corresponding parameters of continuous self-similar sets. There are different notions of growth dimensions of graphs. For a rather general class of self-similar graphs it is proved that all these dimensions coincide and that they can be calculated in the same way as the Hausdorff dimension of continuous self-similar fractals: log µ dim X = log ν. 1.