TY - GEN

T1 - Embedding cycles and paths in a k-ary n-cube

AU - Hsieh, Sun-Yuan

AU - Lin, Tsong Jie

PY - 2007/12/1

Y1 - 2007/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=48049123691&partnerID=8YFLogxK

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U2 - 10.1109/ICPADS.2007.4447775

DO - 10.1109/ICPADS.2007.4447775

M3 - Conference contribution

AN - SCOPUS:48049123691

SN - 9781424418909

T3 - Proceedings of the International Conference on Parallel and Distributed Systems - ICPADS

BT - The 13th International Conference on Parallel and Distributed Systems, ICPADS

T2 - 13th International Conference on Parallel and Distributed Systems, ICPADS

Y2 - 5 December 2007 through 7 December 2007

ER -