Stewart, I. A. and Xiang, Y. (2009) 'Bipanconnectivity and bipancyclicity in k-ary n-cubes.', IEEE transactions on parallel and distributed systems., 20 (1). pp. 25-33.
In this paper we give precise solutions to problems posed by Wang, An, Pan, Wang and Qu and by Hsieh, Lin and Huang. In particular, we show that Q_n^k is bipanconnected and edge-bipancyclic, when k ≥ 3 and n ≥ 2, and we also show that when k is odd, Q_n^k is m-panconnected, for m = (n(k-1)+2k-6)\2, and (k-1)-pancyclic (these bounds are optimal). We introduce a path-shortening technique, called progressive shortening, and strengthen existing results, showing that when paths are formed using progressive shortening then these paths can be efficiently constructed and used to solve a problem relating to the distributed simulation of linear arrays and cycles in a parallel machine whose interconnection network is Q_n^k, even in the presence of a faulty processor.
|Keywords:||Interconnection networks, k-ary n-cubes, Bipanconnectivity, Bipancyclicity.|
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|Publisher Web site:||http://dx.doi.org/10.1109/TPDS.2008.45|
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|Record Created:||09 Jun 2009 16:35|
|Last Modified:||04 Nov 2011 09:34|
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