Embedding various cycles with prescribed paths into -ary -cubes

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• 作者：Yuxing Yang^a ; ^{yxyangcn@163.com} ; ^{yyx@htu.edu.cn} ; Jing Li^b ; Shiying Wang^a
• 关键词：Multiprocessor systems ; Interconnection networks ; kk-ary nn-cubes ; Cycles
• 刊名：Discrete Applied Mathematics
• 出版年：2017
• 出版时间：31 March 2017
• 年：2017
• 卷：220
• 期：Complete
• 页码：161-169
• 全文大小：833 K
• 卷排序：220

文摘

The kk-ary nn-cube has been one of the most popular interconnection networks for large-scale multi-processor systems and data centers. In this study, we investigate the problem of embedding cycles of various lengths passing through prescribed paths in the kk-ary nn-cube. For n≥2n≥2 and k≥5k≥5 with kk odd, we prove that every path with length hh (1≤h≤2n−11≤h≤2n−1) in the kk-ary nn-cube lies on cycles of every length from h+(k−1)(n−1)/2+kh+(k−1)(n−1)/2+k to knkn inclusive.