Edge-pancyclicity of Mobius cubes

The Mobius cube M-n is a variant of the hypercube Q(n) and has better properties than Q(n) with the same number of links and processors. It has been shown by Fan [J. Fan, Hamilton-connectivity and cycle-embedding of Mobius cubes, Inform. Process. Lett. 82 (2002) 113-117] and Huang et al. [W.-T. Huang, W.-K. Chen, C.-H. Chen, Pancyclicity of Mobius 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 2(n). In this paper, we improve this result by showing that every edge of M, lies on a cycle of every length from 4 to 2(n) inclusive. (c) 2005 Elsevier B.V. All rights reserved.