Edge-pancyclicity of Möbius cubes

  • Authors:

  • Min Xu;Jun-Ming Xu

  • Affiliations:

  • Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China and Department of Mathematics, University of Science and Technology of Chi ...;Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, China

  • Venue:
  • Information Processing Letters
  • Year:
  • 2005

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Abstract

The Möbius cube Mn is a variant of the hypercube Qn and has better properties than Qn with the same number of links and processors. It has been shown by Fan [J. Fan, Hamilton-connectivity and cycle-embedding of Möbius cubes, Inform. Process. Lett. 82 (2002) 113-117] and Huang et al. [W.-T. Huang, W.-K. Chen, C.-H. Chen, Pancyclicity of Möbius cubes, in: Proc. 9th Internat. Conf. on Parallel and Distributed Systems (ICPADS'02), 17-20 Dec. 2002, pp. 591-596], independently, that Mn contains a cycle of every length from 4 to 2n. In this paper, we improve this result by showing that every edge of Mn lies on a cycle of every length from 4 to 2n inclusive.