Longest ring and path embedding in faulty hypercube 蘇文彥、洪春男
E-mail: [email protected]
ABSTRACT
In this paper, we show that the adjacency fault tolerance for property 2H of hypercube. We also show that the adjacency fault tolerance for Hamiltonian laceability of hypercube. Applying these results, we can construct a fault-free cycle with length at least 2n-2|Fv|+4 in Qn-Fv where Fv is the faulty vertices set contains at least two black vertices and two white vertices with |Fv|.n. We also construct a fault-free path of length at least 2n-2|Fv|+3 between two different color vertices, and construct the fault-free path with of length at least 2n-2|F_v|+2 between two same color vertices, |Fv| n-1.
Keywords : n-dimensional hypercube, longest cycle, longest path.
Table of Contents
封面內頁 簽名頁 授權書...iii 中文摘要...iv 英文摘
要...v 誌謝...vi 目錄...vii 圖目 錄...viii Chapter 1 Introduction...1 Chapter 2
Preliminaries...4 Chapter 3 The adjacency property 2H of hypercube...6 Chapter 4 The adjacency Hamiltonian laceable of hypercube...15 Chapter 5 The Longest ring in faulty hypercube...27 Section 5.1. Hamiltonian cycle...27 Section 5.2. Fault-free cycle...28 Chapter 6 The Longest path in faulty
hypercub...30 Section 6.1. between two different color vertice...30 Section 6.2. between two same color vertice...32 Chapter 7 Conclusion...36 References...37 REFERENCES
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