Parallel and Distributed Systems, International Conference on (2007)

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–y path of every length from [k/2]n to k<sup>n</sup> − 1, where n ≥ 2 is an integer and k ≥ 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 ≥ 2 is an integer and k ≥ 2 is an even integer.

INDEX TERMS

null

CITATION

null Sun-Yuan Hsieh,
null Tsong-Jie Lin,
"Embedding cycles and paths in a k-ary n-cube",

*Parallel and Distributed Systems, International Conference on*, vol. 01, no. , pp. 1-7, 2007, doi:10.1109/ICPADS.2007.4447775