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Pancyclicity of Matching Composition Networks under the Conditional Fault Model
February 2012 (vol. 61 no. 2)
pp. 278-183
Chia-Wei Lee, National Cheng Kung University, Tainan
Sun-Yuan Hsieh, National Cheng Kung University, Tainan
A graph $G=(V,E)$ is said to be \emph{conditional k-edge-fault pancyclic} if, after removing $k$ faulty edges from $G$ and provided that each node is incident to at least two fault-free edges, the resulting graph contains a cycle of every length from its girth to $|V|$ inclusive. In this paper, we sketch the common properties of a class of networks called Matching Composition Networks (MCNs), such that the conditional edge-fault pancyclicity of MCNs can be determined from the derived properties. We then apply our technical theorem to show that an $m$-dimensional hyper-Petersen network is conditional $(2m-5)$-edge-fault pancyclic. \\ \noindent{\bf Keywords}: Conditional edge faults, fault-tolerant cycle embedding, matching composition networks, pancyclicity, multiprocessor systems.
Index Terms:
Network problems, Path and circuit problems
Citation:
Chia-Wei Lee, Sun-Yuan Hsieh, "Pancyclicity of Matching Composition Networks under the Conditional Fault Model," IEEE Transactions on Computers, vol. 61, no. 2, pp. 278-183, Feb. 2012, doi:10.1109/TC.2010.229
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