Structure of spanning trees on the two-dimensional Sierpinski gasket

Shu-Chiuan Chang, Lung Chi Chen

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Consider spanning trees on the two-dimensional Sierpinski gasket SG(n) where stage n is a non-negative integer. For any given vertex x of SG(n), we derive rigorously the probability distribution of the degree j ε f1; 2; 3; 4g at the vertex and its value in the infinite n limit. Adding up such probabilities of all the vertices divided by the number of vertices, we obtain the average probability distribution of the degree j. The corresponding limiting distribution Φj gives the average probability that a vertex is connected by 1, 2, 3 or 4 bond(s) among all the spanning tree configurations. They are rational numbers given as Φ1 = 10957=40464, Φ2 = 6626035=13636368, Φ3 = 2943139=13636368, Φ4 = 124895=4545456.

Original languageEnglish
Pages (from-to)151-176
Number of pages26
JournalDiscrete Mathematics and Theoretical Computer Science
Volume12
Issue number3
Publication statusPublished - 2010 Dec 6

Fingerprint

Sierpinski Gasket
Spanning tree
Probability distributions
Probability Distribution
Vertex of a graph
Limiting Distribution
Non-negative
Configuration
Integer

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)
  • Discrete Mathematics and Combinatorics

Cite this

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abstract = "Consider spanning trees on the two-dimensional Sierpinski gasket SG(n) where stage n is a non-negative integer. For any given vertex x of SG(n), we derive rigorously the probability distribution of the degree j ε f1; 2; 3; 4g at the vertex and its value in the infinite n limit. Adding up such probabilities of all the vertices divided by the number of vertices, we obtain the average probability distribution of the degree j. The corresponding limiting distribution Φj gives the average probability that a vertex is connected by 1, 2, 3 or 4 bond(s) among all the spanning tree configurations. They are rational numbers given as Φ1 = 10957=40464, Φ2 = 6626035=13636368, Φ3 = 2943139=13636368, Φ4 = 124895=4545456.",
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Structure of spanning trees on the two-dimensional Sierpinski gasket. / Chang, Shu-Chiuan; Chen, Lung Chi.

In: Discrete Mathematics and Theoretical Computer Science, Vol. 12, No. 3, 06.12.2010, p. 151-176.

Research output: Contribution to journalArticle

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