Bipancyclicity in k-ary n-cubes with faulty edges under a conditional fault assumption
Xiang, Y.; Stewart, I.A.
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.
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|
|Publisher||Institute of Electrical and Electronics Engineers|
|Peer Reviewed||Peer Reviewed|
|Keywords||Interconnection networks. k-ary n-cubes. Fault-tolerance. Bipancyclicity.|
Accepted Journal Article
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