The study of Adjacent Vertex-Fault-Tolerance for Hamiltonian cycle passing through prescribed edges of Hypercube
賴映潔、洪春男
E-mail: [email protected]
ABSTRACT In this thesis, we consider the problem of a fault-tolerance Hamiltonian cycle passing through prescribed edges in hypercube Qn with some adjacently faulty vertices.
Let Fe ?} E(Qn) be a set of faulty edges, Fa be a set of adjacently faulty vertices, E0 ?} E(Qn ? Fe ? Fa) be the set of prescribed edges where the subgraph induced by E0 is a linear forest(i.e., pairwise vertex-disjoint paths). We construct a Hamiltonian cycle of Qn ? Fe ? Fa passing through all edges of E0 for any | E0 | ?T 2n ? 4 ? 2| Fe | ? 2| Fa | and | Fe | + | Fa | ?T n – 2, for n ?d 3.
We furthermore show that a Hamiltonian cycle of Qn ? Fe ? Fa passing through all edges of E0 for 1 ?T | E0 | ?T 2n – 3 ? 2| Fe | ? 2| Fa | if n ?d 5.
Keywords : hypercube、prescribed edge、adjacently faulty vertices、fault-tolerance Table of Contents
封面內頁 簽名頁 授權書 iii ABSTRACT iv 中文摘要 v 誌謝 vi 目錄 vii 圖目錄 viii
Chapter 1. Introduction 1 Chapter 2. Preliminaries 3
Chapter 3. The Hamiltonian cycle passing through prescribed edges in hypercubes with adjacently faulty vertices 7
3.1 The initial result 7 3.2 The optimum result 12 Chapter 4. Conclusion 26 Reference 27
Appendix 29 REFERENCES
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