Issue No. 04 - April (2009 vol. 20)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TPDS.2008.123
Sun-Yuan Hsieh , National Cheng Kung University, Tainan
Chia-Wei Lee , National Cheng Kung University, Tainan
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
S. Hsieh and C. Lee, "Conditional Edge-Fault Hamiltonicity of Matching Composition Networks," in IEEE Transactions on Parallel & Distributed Systems, vol. 20, no. , pp. 581-592, 2008.