Adjacent Vertices Fault-tolerance Hamiltonian Laceability of Hypercube 張佾驊、洪春男
E-mail: [email protected]
ABSTRACT
Let Qn be n-dimensional hypercube. In this thesis, we show that Qn – F is Hamiltonian laceable where F is the set of f (n–3) pairs of adjacent faulty vertices and (n–2–f) faulty edges. We also show that Qn – F is hyper-Hamiltonian laceable where F is the set of f (n–3) pairs of adjacent faulty vertices and (n–3–f) faulty edges. Applying these results, we can construct the fault-free path between s, t with at least 2n – 2f’ + 1 for s, t are different color and 2n – 2f’ for s, t are the same color in Qn – F’
where 2 |F’| = f’ (n–2) and F’ is the faulty vertices set contains at least a black vertex and a white vertex. And we can construct the fault-free cycle with at least 2n – 2f’ + 2 in Qn – F’ where 2 |F’| = f’ (n–1) and F’ is the faulty vertices set contains at least a black vertex and a white vertex. The best result thus far is the length 2n – 2f’.
Keywords : n-dimensional hypercube, Hamiltonian laceable, hyper-Hamiltonian laceable.
Table of Contents
封面內頁 簽名頁 授權頁...iii 中文摘要... vi 英 文摘要... v 誌謝... vi 目
錄...vii 圖目錄...viii Chapter 1. Introductions and Definitions... 1 Chapter 2. Preliminaries... 4 Chapter 3. The f-adjacency k Edges Hamiltonian Laceability of Hypercube 3.1 f-adjacency Hamiltonian laceable of Hypercube ... 7 3.2 f-adjacency hyper-Hamiltonian laceable of Hypercube... 18 Chapter 4. Ring Embedding in Hypercube with Faulty Vertices 4.1 Fault-free cycle in Hypercube... 26 4.2 Fault-free path in Hypercube ... 28 Chapter 5. Conclusions and Future Works... 34 References... 35
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