The Number of Spanning Trees in Self-Similar Graphs

2011 ◽  
Vol 15 (2) ◽  
pp. 355-380 ◽  
Author(s):  
Elmar Teufl ◽  
Stephan Wagner
Keyword(s):  
Spanning Trees ◽  
Self Similar ◽  
Number Of Spanning Trees

scholarly journals Spanning trees of finite Sierpiński graphs

2006 ◽  
Vol DMTCS Proceedings vol. AG,... (Proceedings) ◽  
Author(s):  
Elmar Teufl ◽  
Stephan Wagner
Keyword(s):  
Spanning Trees ◽  
Dynamical Behavior ◽  
The Self ◽  
3 Dimensional ◽  
Sierpiński Graphs ◽  
Polynomial Map ◽  
International Audience ◽  
Self Similar ◽  
Number Of Spanning Trees

International audience 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.

scholarly journals The number of spanning trees of an infinite family of outerplanar, small-world and self-similar graphs

2013 ◽  
Vol 392 (12) ◽  
pp. 2803-2806 ◽  
Author(s):  
Francesc Comellas ◽  
Alícia Miralles ◽  
Hongxiao Liu ◽  
Zhongzhi Zhang
Keyword(s):  
Spanning Trees ◽  
Infinite Family ◽  
Small World ◽  
Self Similar ◽  
Number Of Spanning Trees

scholarly journals Asymptotic enumeration on self-similar graphs with two boundary vertices

2009 ◽  
Vol Vol. 11 no. 1 (Combinatorics) ◽  
Author(s):  
Elmar Teufl ◽  
Stephan Wagner
Keyword(s):  
Spanning Trees ◽  
General Setting ◽  
Scaling Factor ◽  
Asymptotic Enumeration ◽  
Spanning Forests ◽  
International Audience ◽  
Self Similar ◽  
Connected Subgraphs ◽  
Graph Parameters ◽  
Number Of Spanning Trees

Combinatorics International audience We study two graph parameters, namely the number of spanning forests and the number of connected subgraphs, for self-similar graphs with exactly two boundary vertices. In both cases, we determine the general behavior for these and related auxiliary quantities by means of polynomial recurrences and a careful asymptotic analysis. It turns out that the so-called resistance scaling factor of a graph plays an essential role in both instances, a phenomenon that was previously observed for the number of spanning trees. Several explicit examples show that our findings are likely to hold in an even more general setting.

Resistance Scaling and the Number of Spanning Trees in Self-Similar Lattices

2011 ◽  
Vol 142 (4) ◽  
pp. 879-897 ◽  
Author(s):  
Elmar Teufl ◽  
Stephan Wagner
Keyword(s):  
Spanning Trees ◽  
Self Similar ◽  
Number Of Spanning Trees

scholarly journals Properties of Commuting Graphs over Semidihedral Groups

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 103
Author(s):  
Tao Cheng ◽  
Matthias Dehmer ◽  
Frank Emmert-Streib ◽  
Yongtao Li ◽  
Weijun Liu
Keyword(s):  
Spanning Trees ◽  
Laplacian Spectrum ◽  
Vertex Connectivity ◽  
Laplacian Energy ◽  
Number Of Spanning Trees

This paper considers commuting graphs over the semidihedral group SD8n. We compute their eigenvalues and obtain that these commuting graphs are not hyperenergetic for odd n≥15 or even n≥2. We further compute the Laplacian spectrum, the Laplacian energy and the number of spanning trees of the commuting graphs over SD8n. We also discuss vertex connectivity, planarity, and minimum disconnecting sets of these graphs and prove that these commuting graphs are not Hamiltonian.

scholarly journals On the characterization of graphs with maximum number of spanning trees

1998 ◽  
Vol 179 (1-3) ◽  
pp. 155-166 ◽  
Author(s):  
L. Petingi ◽  
F. Boesch ◽  
C. Suffel
Keyword(s):  
Spanning Trees ◽  
Number Of Spanning Trees
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