Enumeration problems for classes of self-similar graphs
Journal of Combinatorial Theory Series A
Quantifying the Degree of Self-Nestedness of Trees: Application to the Structural Analysis of Plants
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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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: ${\rm dim}\ X={{\rm log}\ \mu \over {\rm log}\ \nu }$. © 2004 Wiley Periodicals, Inc. J Graph Theory 45: 224–239, 2004