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

Xiang, Y.; Stewart, I.A.

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: Nov 4, 2010
• Journal: IEEE Transactions on Parallel and Distributed Systems
• Print ISSN: 1045-9219
• Electronic ISSN: 1558-2183
• 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.
• Public URL: https://durham-repository.worktribe.com/output/1537919
• Publisher URL: http://www.dur.ac.uk/i.a.stewart/Papers/Bipancyckaryncubesundercfa.pdf