Mathematics – Combinatorics
Scientific paper
2002-02-18
Mathematics
Combinatorics
14 pages, 3 figures
Scientific paper
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 $\nu$ and the volume scaling factor $\mu$ 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: \[\dim X=\frac{\log \mu}{\log \nu}.\]
No associations
LandOfFree
Growth of self-similar graphs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Growth of self-similar graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Growth of self-similar graphs will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-161857