| 研究生: |
林育丞 Yu-Cheng Lin |
|---|---|
| 論文名稱: |
d 維立方體圖上有效電阻與首達時間的計算方法 On the computation of effective resistances and first hitting time in a d-cube |
| 指導教授: |
葉鴻國
Hong-Gwa Yeh |
| 口試委員: | |
| 學位類別: |
碩士 Master |
| 系所名稱: |
理學院 - 數學系 Department of Mathematics |
| 論文出版年: | 2018 |
| 畢業學年度: | 106 |
| 語文別: | 英文 |
| 論文頁數: | 19 |
| 中文關鍵詞: | 圖論 、首達時間 |
| 外文關鍵詞: | Graph Theory, Hitting Time |
| 相關次數: | 點閱:11 下載:0 |
| 分享至: |
| 查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
在這份報告中,我們整理了學界已發表的論文中,用來計算 d 維立方體圖中兩點間有效電阻與首達時間的一些方法。
In this report, we present several known methods in the literature which determine the first hitting time and resistance distances between two nodes in a d-dimensional hypercube (d-cube).
[1] Titu Andreescu and Răzvan Gelca, Mathematical Olympiad challenges, Birkhäuser, 2000.
[2] Béla Bollobás, Modern Graph Theory, Graduate Texts in Mathematics, vol. 184, Springer, 1998.
[3] P. Doyle and J. Snell, Random walks and electric networks, The Mathematical Association of
America, vol. 22, 1987.
[4] L. Lovász, Random walks on graphs: a survey, in combinatorics, Paul Erdös is eighty, Bolyai
Soc. Math. Stud. 2 (1993) 1-46.
[5] Daniel A. Spielman, Course Notes for Spectral Graph Theory - Lecture 5, Fall 2014, Yale University,
USA.
[6] Daniel A. Spielman, Course Notes for Spectral Graph Theory - Lectures 7 and 8, Fall 2015, Yale
University, USA.
[7] P. Tetali, Random walks and the effective resistance of networks, J. Theoret. Probab. 4 (1991)
101-109.
[8] O. J. Tretiak and T. S. Huang, Resistance of an n-dimensional cube, Proceedings of the IEEE,
Volume: 53, Issue: 9 (1965) 1271-1272
[9] Hong-Gwa Yeh, Class Notes for Graph Structure Theory, Fall 2016, National Central University,
Taiwan.