Fault-Tolerant Super-Hamiltonicity ot the Cartesian Product Graph

• Main Authors: Jiun-Ji Chen, 陳俊吉
• Other Authors: Sun-Yuan Hsieh
• Format: Others
• Language: en_US
• Published: 2006
• Online Access: http://ndltd.ncl.edu.tw/handle/40949329547161452637

碩士 === 國立成功大學 === 資訊工程學系碩博士班 === 94 === 　　A k-regular Hamiltonian and Hamiltonian connected graph is called super fault-tolerant Hamiltonian if and only if it remains Hamiltonian after removing at most k - 2 nodes and/or edges and remains Hamiltonian connected after removing at most k - 3 nodes and/or edges. A super fault-tolerant Hamiltonian graph has a certain optimal favor with respect to the fault-tolerant Hamiltonicity and Hamiltonian connectivity. In this thesis, we investigate a method to find Hamiltonian cycles and Hamiltonian connectivity in graphs constructed by Cartesian product from any two super fault-tolerant Hamiltonian graph. Therefore, the Cartesian product of two super fault-tolerant Hamiltonian graph is also a super fault-tolerant Hamiltonian graph.