Embedding even-length cycles in a hexagonal honeycomb mesh

Authors:
Xiaofan Yang;Yuan Yan Tang;Jianqiu Cao;Qing Lu
Affiliations:
College of Computer Science, Chongqing University, Chongqing, China,School of Computer and Information, Chongqing Jiaotong University, Chongqing, China;College of Computer Science, Chongqing University, Chongqing, China;School of Computer and Information, Chongqing Jiaotong University, Chongqing, China;Department of Chemistry, Eighth Senior School, Chongqing, China
Venue:
International Journal of Computer Mathematics
Year:
2008

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Abstract

The existence and construction of cycles of various lengths in an interconnection network are important issues in efficiently executing ring-structured parallel algorithms in such a network. The hexagonal honeycomb mesh (HHM) is regarded as a promising candidate for interconnection networks. In this paper we address the problem of how to embed even-length cycles in an HHM. We prove that an HHM of order t≥3 admits a cycle of length l for each even number l such that l=6 or 10≤l≤6t2-2. We also describe a systematic method for building these cycles.