The Study of Edge Fault-Tolerance for Hamiltonian Cycles and Hamiltonian Paths Passing through Prescribed Edges of Star
游宗育、洪春男
E-mail: [email protected]
ABSTRACT
The star graph is a famous interconnection network. In this thesis, we discuss the edge fault tolerance for Hamiltonian cycle and Hamiltonian path passing through prescribed edges for star graph. Let F_e be the set of faulty edges of S_n and E_0 be the edge set of some pairwise vertex-disjoint paths of S_n. At first, we prove all edges of E_0 lie on a Hamiltonian cycle of S_n-F_e, if |F_e| ? n?3, |E_0| ? 2n?5?2|F_e| and lie on a Hamiltonian path P(u, v) where d(u, v) is odd, |F_e| ? n?3, |E_0| ? 2n?7?2|F_e|. After, we improve the result of more prescribed edges, we show lie on a Hamiltonian path P(u, v) where d(u, v) is odd, |F_e| ? n?3, |E_0| ? 2n?6?2|F_e|.
Keywords : star graph、fault tolerance、Hamiltonian cycle、Hamiltonian path、prescribed edges Table of Contents
封面內頁 簽名頁 ABSTRACT………
………iii 中文摘要………
…………iv 誌謝………
……v 目錄………
…vi 圖目錄………vii 表目錄………ix Chapter1 Introduction………1 Chapter2 Definitions and Basic Properties………4 Chapter3 Hamiltonian cycles and paths passing through prescribed Edges………6 Chapter4 Hamiltonian paths passing through more prescribed Edges………26 Chapter5 Conclusion ………
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