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The Computer Journal Advance Access published online on April 21, 2009
The Computer Journal, doi:10.1093/comjnl/bxp027
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© The Author 2009. Published by Oxford University Press on behalf of The British Computer Society. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

The Bipancycle-Connectivity and the m-Pancycle-Connectivity of the k-ary n-cube

Jywe-Fei Fang*

Department of Digital Content and Technology, National Taichung University, 140 Min-Shen Road, Taichung 403, Taiwan, ROC

* Corresponding author: jffang{at}mail.ntcu.edu.tw

Received 11 October 2008; revised 27 March 2009

The interconnection network considered in this paper is the k-ary n-cube that is an attractive variance of the well-known hypercube. Many interconnection networks that are desirable in both theoretical interests and practical systems, including the ring, torus and hypercube, may be regarded as the subclasses of k-ary n-cubes. In this paper, we investigate the pancycle-connected properties of the k-ary n-cube. We show that the k-ary n-cube is bipancycle-connected for k being even. That is, each pair of vertices x and y is contained by a cycle of each even length ranging from the length of the smallest even cycle that contains x and y to N, where N is the order of the network. We also show that the k-ary n-cube is strictly m-pancycle-connected for k being odd and n ≥ 2, where m = nk - n. That is, each pair of vertices is contained by a cycle of each length ranging from nk - n to N; and nk - n has reached the lower bound of the problem.

Key Words: interconnection networks • k-ary n-cubes • m-pancycle-connectivity • bipancycle-connectivity

Handling editor: Alberto Apostolico


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