Conditional Edge-Fault Hamiltonicity of Cartesian Product Graph

• Main Authors: Chia-Wen Cheng, 鄭嘉文
• Other Authors: 謝孫源
• Format: Others
• Language: en_US
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/08366465385493194785

碩士 === 國立成功大學 === 資訊工程學系碩博士班 === 97 === A graph G is called conditional k-edge-fault Hamiltonian if after deleting at most k edges from G and each vertex is incident to at least two fault-free edges, the resulting graph remains Hamiltonian. Given two graph G and H, let k1 and k2 be the positive integers such that k1=δ(G)≧3, k2=δ(H)≧3. If G is Hamiltonian-connected, (k1-2)-edge-fault adjacency-Hamiltonian-connected, and conditional (2k1-5)-edge-fault Hamiltonian; H is Hamiltonian-connected, (k2-2)-edge-fault adjacency-Hamiltonian-connected, and conditional (2k2-5)-edge-fault Hamiltonian. Then, we show that the Cartesian product network G×H is (2k1+2k2-5)-edge-fault Hamiltonian. We then apply our result to determine the conditional edge-fault Hamiltonicity of one multiprocessor system, the nearest neighbor mesh hypercube, belong to Cartesian networks.