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

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	Similar Articles Articles by null Sun-Yuan Hsieh Articles by null Tsong-Jie Lin

13th International Conference on Parallel and Distributed Systems - Volume 1 (ICPADS'07)

Hsinchu, Taiwan

December 05-December 07

ISBN: 978-1-4244-1889-3

	ASCII Text	x
	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. 1, pp. 1-7, 13th International Conference on Parallel and Distributed Systems - Volume 1 (ICPADS'07), 2007.

	BibTex	x
	@article{ 10.1109/ICPADS.2007.4447775, author = {null Sun-Yuan Hsieh and null Tsong-Jie Lin}, title = {Embedding cycles and paths in a k-ary n-cube}, journal ={Parallel and Distributed Systems, International Conference on}, volume = {1}, year = {2007}, isbn = {978-1-4244-1889-3}, pages = {1-7}, doi = {http://doi.ieeecomputersociety.org/10.1109/ICPADS.2007.4447775}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }

	RefWorks Procite/RefMan/Endnote	x
	TY - CONF JO - Parallel and Distributed Systems, International Conference on TI - Embedding cycles and paths in a k-ary n-cube SN - 978-1-4244-1889-3 SP1 EP7 A1 - null Sun-Yuan Hsieh, A1 - null Tsong-Jie Lin, PY - 2007 KW - null VL - 1 JA - Parallel and Distributed Systems, International Conference on ER -

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

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/ICPADS.2007.4447775

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

Citation:

null Sun-Yuan Hsieh, null Tsong-Jie Lin, "Embedding cycles and paths in a k-ary n-cube," icpads, vol. 1, pp.1-7, 13th International Conference on Parallel and Distributed Systems - Volume 1 (ICPADS'07), 2007

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