Hamiltonian cycles passing through linear forests in k-ary n-cubes

Authors:
Shiying Wang;Yuxing Yang;Jing Li;Shangwei Lin
Affiliations:
School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, PR China;School of Computer and Information Technology, Shanxi University, Taiyuan, Shanxi 030006, PR China and School of Computer and Information Engineering, Anyang Normal University, Anyang, Henan 45500 ...;School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, PR China;School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, PR China
Venue:
Discrete Applied Mathematics
Year:
2011

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Abstract

The k-ary n-cube is one of the most popular interconnection networks for parallel and distributed systems. A linear forest in a graph is a subgraph, each component of which is a path. In this paper, we investigate the existence of Hamiltonian cycles passing through linear forests in the k-ary n-cube. For any n=2 and k=3, we show that the k-ary n-cube admits a Hamiltonian cycle passing through a linear forest with at most 2n-1 edges.