Panconnectivity of locally twisted cubes

The locally twisted cube LTQn which is a newly introduced interconnection network for parallel computing is a variant of the hypercube QnQn. Yang et al. [X. Yang, G.M. Megson, D.J. Evans, Locally twisted cubes are 4-pancyclic, Applied Mathematics Letters 17 (2004) 919–925] proved that LTQn is Hamiltonian connected and contains a cycle of length from 4 to 2n2n for n≥3n≥3. In this work, we improve this result by showing that for any two different vertices uu and vv in LTQn (n≥3n≥3), there exists a uvuv-path of length ll with d(u,v)+2≤l≤2n−1d(u,v)+2≤l≤2n−1 except for a shortest uvuv-path.