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 Qn. 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 2 n for n ≥ 3. In this work, we improve this result by showing that for any two different vertices u and v in LTQn (n ≥ 3), there exists a uv-path of length l with d(u ,v )+ 2 ≤ l ≤ 2 n − 1 except for a shortest uv-path. c

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