Panconnectivity of locally twisted cubes

Abstract

The locally twisted cube LTQ n which is a newly introduced interconnection network for parallel computing is a variant of the hypercube Q n . 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 LTQ n 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 LTQ n ( n ≥ 3 ), there exists a u v -path of length l with d ( u , v ) + 2 ≤ l ≤ 2 n − 1 except for a shortest u v -path.