DOAJ Open Access 2006

Spanning trees of finite Sierpiński graphs

Elmar Teufl Stephan Wagner

Lihat Sumber DOI

Abstrak

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.

Topik & Kata Kunci

Mathematics

Penulis (2)

Elmar Teufl

Stephan Wagner

Format Sitasi

APA MLA BibTeX

Teufl, E., Wagner, S. (2006). Spanning trees of finite Sierpiński graphs. https://doi.org/10.46298/dmtcs.3494

Akses Cepat

Lihat di Sumber doi.org/10.46298/dmtcs.3494

Informasi Jurnal

Tahun Terbit: 2006
Sumber Database: DOAJ
DOI: 10.46298/dmtcs.3494
Akses: Open Access ✓