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, China;Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, China;Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, China

  • Venue:
  • Information Processing Letters
  • Year:
  • 2006

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Abstract

The Möbius cube MQn and the crossed cube CQn are two important variants of the hypercube Qn. This paper shows that for any two different vertices u and v in G ∈ {MQn, CQn} with n ≥ 3, there exists a uv-path of every length from dG(u, v) + 2 to 2n - 1 except for a shortest uv-path, where dG(u, v) is the distance between u and v in G. This result improves some known results.