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研究生:錢奕儒
研究生(外文):Yi-Ru Cian
論文名稱:擴增立方體之條件邊容錯漢彌爾頓性質
論文名稱(外文):Conditional Fault-Tolerant Hamiltonicity of Augmented Cubes
指導教授:謝孫源
指導教授(外文):Sun-Yuan Hsieh
學位類別:碩士
校院名稱:國立成功大學
系所名稱:資訊工程學系碩博士班
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2008
畢業學年度:96
語文別:英文
論文頁數:61
中文關鍵詞:擴增立方體漢彌爾頓性質.漢彌爾頓圓圈容錯
外文關鍵詞:fault-tolerantHamiltonicity.Hamiltonian cyclesAugmented cube
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  • 下載下載:11
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擴增立方體(augmented cube)是超立方體(hypercube)的一種變形,其中擁有某些優於超立方體的特性。在這篇論文中,我們研究擴增立方體的邊容錯漢彌爾頓性質(edge-fault-tolerant Hamiltonicity)
。我們將證明在每個節點均連接兩條以上好邊的擴增立方體中,當錯邊個數不超過4n-8,在圖形裡可以找到一條健康(fault-free)的漢彌爾頓圓圈(Hamiltonian cycle)。同時,我們也證明論文中能容忍的錯邊個數是最佳的
The augmented cube is a variation of hypercubes, which possesses some properties superior to the hypercubes. In this thesis, we show that, for any n-dimensional augmented cube (n>=3) with at most 4n-8 faulty edges in which each vertex is incident to at least two fault-free edges, there exists a fault-free Hamiltonian cycle. We also demonstrate that our result is optimal with respect to the number of faulty edges tolerated.
Abstract(in Chinese) i
Abstract ii
Acknowledgement iii
Contents v
List of Figures vi
1 Introduction 1
2 Preliminaries 3
3 Two Special Cases 33
4 The General Case 37
5 Concluding Remarks 57
Bibliography 59
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