Edge-pancyclicity of Möbius cubes

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.  2005 Elsevier B.V. All rights reserved.