Xiang, Y. and Stewart, I.A. (2011) 'Bipancyclicity in k-ary n-cubes with faulty edges under a conditional fault assumption.', IEEE transactions on parallel and distributed systems., 22 (9). pp. 1506-1513.
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.
|Keywords:||Interconnection networks. k-ary n-cubes. Fault-tolerance. Bipancyclicity.|
|Full text:||(AM) Accepted Manuscript|
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|Publisher Web site:||http://dx.doi.org/10.1109/TPDS.2011.22|
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|Date accepted:||No date available|
|Date deposited:||04 November 2010|
|Date of first online publication:||2011|
|Date first made open access:||No date available|
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