Growth of self-similar graphs

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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: \[\dim X=\frac{\log μ}{\log ν}.\]
14 pages, 3 figures

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Combinatorics, 05C12, 28A80

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http://salesiana.dossiersoluciones.com/handle/123456789/63365

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0202171
 http://arxiv.org/abs/math/0202171

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arXiv