Lower bound of the asymptotic complexity of self-similar fractal graphs

Abstract

We study the asymptotic complexity constant of the sequence of approximating graphs to a fully symmetric self-similar structure on a finitely ramified fractal $K$. We show how full symmetry implies existence of the asymptotic complexity constant and obtain a sharp lower bound thereby answering two conjectures by Anema.

12 pages. arXiv admin note: text overlap with arXiv:1211.7341 by other authors

References in corpus (3)

• Spanning trees on the Sierpinski gasket
• Some Exact Results for Spanning Trees on Lattices
• Counting Spanning Trees on Fractal Graphs