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| 研究生： |
林宏穎 Hong-Ying Lin |
|---|---|
| 論文名稱： |
控制理論觀點的有向圖電阻距離簡介 Introduction to Resistance Distance for Digraphs from Control Theory Perspective |
| 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： | 2021 |
| 畢業學年度： | 109 |
| 語文別： | 英文 |
| 論文頁數： | 59 |
| 中文關鍵詞： | 有效電阻 |
| 相關次數： | 點閱：5 下載：0 |
| 分享至: |
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在2016 年，Young，Scardovi 和Leonard [10] 的文章中，他們在邊加權的有向圖上，對圖中兩個不同的節點i 和j 定義了有效電阻rij 的新概念。在此碩士論文中，我們主要的工作是蒐集用來了解rij 定義的基礎知識並證明必要的數學理論。在論文的最後，我們透過Python程式計算一些特殊有向圖上的有效電阻，以提供有向圖結構對rij 影響的線索。
In [10], Young, Scardovi and Leonard gave a definition of effective resistance rij for two distinct nodes i and j in an edge-weighted directed graph. In this report we describe basic knowledge and develop necessary tools to understand their interesting definition of effective resistance in directed
graphs.
References
[1] Richard Bellman, Introduction to Matrix Analysis, SIAM, Philadelphia, Reprint of the Second edition, 1995.
[2] J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, North Holland, Amsterdam,1976.
[3] J. A. Bondy and U. S. R. Murty, Graph Theory, Springer, 2008.
[4] Z. Gajic and M.T.J. Qureshi, Lyapunov Matrix Equation in System Stability and Control, Dover Books on Engineering Series. Dover Publications, 2008.
[5] Roger A. Horn and Charles R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge,UK, second edition, 2012.
[6] Alan J. Laub, Matrix Analysis for Scientists and Engineers, 2004, SIAM, Philadelphia.
[7] C.D. Meyer, Matrix Analysis and Applied Linear Algebra, 2000, SIAM, Philadelphia.
[8] William J. Terrell, Stability and Stabilization: An Introduction, 2009, Princeton University Press.
[9] Hong-Gwa Yeh, Class Notes for Graph Theory, Fall 2020 and Spring 2021, National Central University, Taiwan.
[10] George Forrest Young, Luca Scardovi and Naomi Ehrich Leonard, A New Notation of Effective Resistance for Directed Graphs - Part I: Definition and Properties, IEEE Transactions on Automatic Control, 61 (2016) 1727-1736.
