### 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 Φ_{j} 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 Φ_{1} = 10957=40464, Φ_{2} = 6626035=13636368, Φ_{3} = 2943139=13636368, Φ_{4} = 124895=4545456.

Original language | English |
---|---|

Pages (from-to) | 151-176 |

Number of pages | 26 |

Journal | Discrete Mathematics and Theoretical Computer Science |

Volume | 12 |

Issue number | 3 |

Publication status | Published - 2010 Dec 6 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

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

### Cite this

*Discrete Mathematics and Theoretical Computer Science*,

*12*(3), 151-176.

}

*Discrete Mathematics and Theoretical Computer Science*, vol. 12, no. 3, pp. 151-176.

**Structure of spanning trees on the two-dimensional Sierpinski gasket.** / Chang, Shu-Chiuan; Chen, Lung Chi.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Structure of spanning trees on the two-dimensional Sierpinski gasket

AU - Chang, Shu-Chiuan

AU - Chen, Lung Chi

PY - 2010/12/6

Y1 - 2010/12/6

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=78649625030&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78649625030&partnerID=8YFLogxK

M3 - Article

VL - 12

SP - 151

EP - 176

JO - Discrete Mathematics and Theoretical Computer Science

JF - Discrete Mathematics and Theoretical Computer Science

SN - 1365-8050

IS - 3

ER -