Growth of self-similar graphs
| dc.creator | Krön, Bernhard | |
| dc.date | 2002-02-18 | |
| dc.date | 2002-09-12 | |
| dc.date.accessioned | 2026-07-07T04:46:31Z | |
| dc.date.available | 2026-07-07T04:46:31Z | |
| dc.description | 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: \[\dim X=\frac{\log μ}{\log ν}.\] | |
| dc.description | 14 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/math/0202171 | |
| dc.identifier | http://arxiv.org/abs/math/0202171 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63365 | |
| dc.subject | Combinatorics | |
| dc.subject | 05C12, 28A80 | |
| dc.title | Growth of self-similar graphs | |
| dc.type | text |