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

Xiang, Y.; Stewart, I.A.

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


Authors

Y. Xiang



Abstract

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.

Citation

Xiang, Y., & Stewart, I. (2011). Bipancyclicity in k-ary n-cubes with faulty edges under a conditional fault assumption. IEEE Transactions on Parallel and Distributed Systems, 22(9), 1506-1513. https://doi.org/10.1109/tpds.2011.22

Journal Article Type Article
Publication Date Sep 1, 2011
Deposit Date Oct 28, 2010
Publicly Available Date Mar 28, 2024
Journal IEEE Transactions on Parallel and Distributed Systems
Print ISSN 1045-9219
Publisher Institute of Electrical and Electronics Engineers
Peer Reviewed Peer Reviewed
Volume 22
Issue 9
Pages 1506-1513
DOI https://doi.org/10.1109/tpds.2011.22
Keywords Interconnection networks. k-ary n-cubes. Fault-tolerance. Bipancyclicity.
Publisher URL http://www.dur.ac.uk/i.a.stewart/Papers/Bipancyckaryncubesundercfa.pdf

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