Issue No. 10 - Oct. (2013 vol. 24)
ISSN: 1045-9219
pp: 1951-1960
Chia-Wen Cheng , National Cheng Kung University, Tainan
Chia-Wei Lee , National Cheng Kung University, Tainan
Sun-Yuan Hsieh , National Cheng Kung University, Tainan
ABSTRACT
A graph $(G)$ is conditional $(k)$-edge-fault Hamiltonian if it remains Hamiltonian after deleting at most $(k)$ edges and each vertex incident to at least two nonfaulty edges. A graph $(G)$ is $(k)$-edge-fault Hamiltonian-connected if it remains Hamiltonian-connected after deleting at most $(k)$ edges. This study shows that the conditional edge-fault Hamiltonicity of the Cartesian product network $(G\times H)$ can be efficiently evaluated given two graphs $(G)$ and $(H)$ that are edge-fault Hamilton-connected and conditional edge-fault Hamiltonian. This study uses the result to evaluate the conditional edge-fault Hamiltonicity of two multiprocessor systems, the generalized hypercubes and the nearest neighbor mesh hypercubes, both of which belong to Cartesian product networks.
INDEX TERMS
Bridges, Hypercubes, Argon, Algorithm design and analysis, Multiprocessing systems, Distributed computing, Educational institutions, graph theoretical interconnection networks, Cartesian product networks, fault-tolerant embedding, Hamiltonicity, Hamiltonian-connectivity
CITATION
Chia-Wen Cheng, Chia-Wei Lee, Sun-Yuan Hsieh, "Conditional Edge-Fault Hamiltonicity of Cartesian Product Graphs", IEEE Transactions on Parallel & Distributed Systems, vol. 24, no. , pp. 1951-1960, Oct. 2013, doi:10.1109/TPDS.2012.304