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Hsinchu, Taiwan
Dec. 5, 2007 to Dec. 7, 2007
ISBN: 978-1-4244-1889-3
pp: 1-7
null Sun-Yuan Hsieh , Department of Computer Science and Information Engineering, National Cheng Kung University, No. 1, University Road, Tainan 701, TAIWAN
null Tsong-Jie Lin , Department of Computer Science and Information Engineering, National Cheng Kung University, No. 1, University Road, Tainan 701, TAIWAN
ABSTRACT
The k-ary n-cube, denoted by Q<inf>n</inf><sup>k</sup>, has been one of the most common interconnection networks. In this paper, we study some topological properties of Q<inf>n</inf><sup>k</sup>. Given two arbitrary distinct nodes x and y in Q<inf>n</inf><sup>k</sup>, we show that there exists an x&#x2013;y path of every length from [k/2]n to k<sup>n</sup> &#x2212; 1, where n &#x2265; 2 is an integer and k &#x2265; 3 is an odd integer. Based on this result, we further show that each edge in Q<inf>n</inf><sup>k</sup> lies on a cycle of every length from k to k<sup>n</sup>. In addition, we show that Q<inf>n</inf><sup>k</sup> is both bipanconnected and edge-bipancyclic, where n &#x2265; 2 is an integer and k &#x2265; 2 is an even integer.
INDEX TERMS
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CITATION
null Sun-Yuan Hsieh, null Tsong-Jie Lin, "Embedding cycles and paths in a k-ary n-cube", ICPADS, 2007, Parallel and Distributed Systems, International Conference on, Parallel and Distributed Systems, International Conference on 2007, pp. 1-7, doi:10.1109/ICPADS.2007.4447775
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