Issue No.04 - April (2009 vol.20)
Sun-Yuan Hsieh , National Cheng Kung University, Tainan
Chia-Wei Lee , National Cheng Kung University, Tainan
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TPDS.2008.123
A graph $G$ is called Hamiltonian if there is a Hamiltonian cycle in $G$. The conditional edge-fault Hamiltonicity of a Hamiltonian graph $G$ is the largest $k$ such that after removing $k$ faulty edges from $G$, provided that each node is incident to at least two fault-free edges, the resulting graph contains a Hamiltonian cycle. In this paper, we sketch common properties of a class of networks, called Matching Composition Networks (MCNs), such that the conditional edge-fault Hamiltonicity of MCNs can be determined from the found properties. We then apply our technical theorems to determine conditional edge-fault Hamiltonicities of several multiprocessor systems, including $n$-dimensional crossed cubes, $n$-dimensional twisted cubes, $n$-dimensional locally twisted cubes, $n$-dimensional generalized twisted cubes, and $n$-dimensional hyper Petersen networks. Moreover, we also demonstrate that our technical theorems can be applied to network construction.
Graph Theory, Network problems, Path and circuit problems
Sun-Yuan Hsieh, Chia-Wei Lee, "Conditional Edge-Fault Hamiltonicity of Matching Composition Networks", IEEE Transactions on Parallel & Distributed Systems, vol.20, no. 4, pp. 581-592, April 2009, doi:10.1109/TPDS.2008.123