Counting spanning trees on fractal graphs and their asymptotic complexity

Autor:	Anema, Jason A., Tsougkas, Konstantinos
Rok vydání:	2016
Předmět:	Mathematics - Combinatorics Mathematics - Spectral Theory
Druh dokumentu:	Working Paper
DOI:	10.1088/1751-8113/49/35/355101
Popis:	Using the method of spectral decimation and a modified version of Kirchhoff's Matrix-Tree Theorem, a closed form solution to the number of spanning trees on approximating graphs to a fully symmetric self-similar structure on a finitely ramified fractal is given in Theorem \ref{thm:maintheoremfull}. We show how spectral decimation implies the existence of the asymptotic complexity constant and obtain some bounds for it. Examples calculated include the Sierpinski Gasket, a non post critically finite analog of the Sierpinski Gasket, the Diamond fractal, and the Hexagasket. For each example, the asymptotic complexity constant is found. Comment: 26 pages. arXiv admin note: substantial text overlap with arXiv:1211.7341
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1602.01996 Zobrazit plný text záznamu View this record from Arxiv