Embedding cycles and paths in a k-ary n-cube

Authors:
Sun-Yuan Hsieh; Tsong-Jie Lin
Affiliations:
Department of Computer Science and Information Engineering, National Cheng Kung University, No. 1, University Road, Tainan 701, TAIWAN;Department of Computer Science and Information Engineering, National Cheng Kung University, No. 1, University Road, Tainan 701, TAIWAN
Venue:
ICPADS '07 Proceedings of the 13th International Conference on Parallel and Distributed Systems - Volume 01
Year:
2007

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Abstract

The k-ary n-cube, denoted by Qnk, has been one of the most common interconnection networks. In this paper, we study some topological properties of Qnk. Given two arbitrary distinct nodes x and y in Qnk, we show that there exists an x–y path of every length from [k/2]n to kn − 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 Qnk lies on a cycle of every length from k to kn. In addition, we show that Qnk is both bipanconnected and edge-bipancyclic, where n ≥ 2 is an integer and k ≥ 2 is an even integer.