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Bipanconnectivity and bipancyclicity in k-ary n-cubes.

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.

Abstract

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.

Item Type:Article
Keywords:Interconnection networks, k-ary n-cubes, Bipanconnectivity, Bipancyclicity.
Full text:PDF - Published Version (1342Kb)
Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1109/TPDS.2008.45
Publisher statement:This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder. ©2009 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Record Created:09 Jun 2009 16:35
Last Modified:04 Nov 2011 09:34

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