Paths in Möbius cubes and crossed cubes

Authors:
Jun-Ming Xu;Meijie Ma;Min Lü
Affiliations:
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026 China;Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026 China;Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026 China
Venue:
Information Processing Letters
Year:
2006

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Abstract

The Mobius cube MQ"n and the crossed cube CQ"n are two important variants of the hypercube Q"n. This paper shows that for any two different vertices u and v in G@?{MQ"n,CQ"n} with n=3, there exists a uv-path of every length from d"G(u,v)+2 to 2^n-1 except for a shortest uv-path, where d"G(u,v) is the distance between u and v in G. This result improves some known results.