## 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 |
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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 |

## All Science Journal Classification (ASJC) codes

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