### Abstract

For any undirected connected graph G = (V, E) with order n, let P ^{(β)} = (p_{uv}^{(β)})_{u,v∈V} be a transition matrix defined by p_{uv}^{(β)} = exp[-βU(u,v)]/∑_{w∈N(u)}exp[-βU(u,w)] for u ∈ V, v ∈ N(u), where β is a real number, N(u) is the set of vertices adjacent to a vertex u, deg(u) = |N(u)|, and U(·, ·) is a potential function defined as U(u, v) = U(v) = log deg(v) for v ∈ N(u), u ∈ V. In this paper, we show that for any undirected graph with order n, the cover time and the mean hitting time for P^{(1/2)} are bounded by O(n^{2} log n) and O(n^{2}), respectively. Since the mean hitting time of a path graph of order n, for any transition matrix, is ω(n^{2}), P^{(1/2)} is best possible with respect to the mean hitting time.

Original language | English |
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Title of host publication | Proceedings of the International Conference on VLSI, VLSI 03 |

Editors | H.R. Arbania, L.T. Yang |

Pages | 203-207 |

Number of pages | 5 |

Publication status | Published - Dec 1 2003 |

Event | Proceedings of the International Conference on VLSI, VLSI'03 - Las Vegas, NV, United States Duration: Jun 23 2003 → Jun 26 2003 |

### Publication series

Name | Proceedings of the International Conference on VLSI |
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### Other

Other | Proceedings of the International Conference on VLSI, VLSI'03 |
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Country | United States |

City | Las Vegas, NV |

Period | 6/23/03 → 6/26/03 |

### All Science Journal Classification (ASJC) codes

- Hardware and Architecture
- Electrical and Electronic Engineering

### Cite this

*Proceedings of the International Conference on VLSI, VLSI 03*(pp. 203-207). (Proceedings of the International Conference on VLSI).