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Bipancyclicity in k-ary n-cubes with faulty edges under a conditional fault assumption.

By Y. Xiang and I.A. Stewart


We prove that a k-ary 2-cube Q^k_2 with 3 faulty edges but where every vertex is incident with at least 2 healthy edges is bipancyclic, if k \geq 3, and k-pancyclic, if k \geq 5 is odd (these results are optimal). We go on to show that when k \geq 4 is even and n \geq 3, any k-ary n-cube Q^k_n with at most 4n − 5 faulty edges so that every vertex is incident with at least 2 healthy edges is bipancyclic, and that this result is optimal

Topics: Interconnection networks. k-ary n-cubes. Fault-tolerance. Bipancyclicity.
Publisher: IEEE Computer Society
Year: 2011
DOI identifier: 10.1109/TPDS.2011.22
OAI identifier: oai:dro.dur.ac.uk.OAI2:7500

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