Spanning trees of finite Sierpiński graphs - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Discrete Mathematics and Theoretical Computer Science Year : 2006

Spanning trees of finite Sierpiński graphs

Abstract

We show that the number of spanning trees in the finite Sierpiński graph of level $n$ is given by $\sqrt[4]{\frac{3}{20}} (\frac{5}{3})^{-n/2} (\sqrt[4]{540})^{3^n}$. The proof proceeds in two steps: First, we show that the number of spanning trees and two further quantities satisfy a $3$-dimensional polynomial recursion using the self-similar structure. Secondly, it turns out, that the dynamical behavior of the recursion is given by a $2$-dimensional polynomial map, whose iterates can be computed explicitly.
Fichier principal
Vignette du fichier
dmAG0135.pdf (146.41 Ko) Télécharger le fichier
Origin : Publisher files allowed on an open archive
Loading...

Dates and versions

hal-01184698 , version 1 (17-08-2015)

Identifiers

Cite

Elmar Teufl, Stephan Wagner. Spanning trees of finite Sierpiński graphs. Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, 2006, Nancy, France. pp.411-414, ⟨10.46298/dmtcs.3494⟩. ⟨hal-01184698⟩

Collections

INSMI TDS-MACS
208 View
563 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More