A note on path embedding in crossed cubes with faulty vertices

Abstract

In this note, we investigate the problem of embedding paths of various lengths into crossed cubes with faulty vertices. In Park et al. (2007) [14] showed that, for any hypercube-like interconnection network of 2n vertices with a set F of faulty vertices and/or edges, there exists a fault-free path of length ℓ between any two distinct fault-free vertices for each integer ℓ satisfying 2n−3⩽ℓ⩽2n−|F|−1. In this note, we show that, for crossed cubes CQn with n⩾5, the range of ℓ can be extended to [2n−5,2n−|F|−1]. Moreover, we also show that the vertices of CQ5 can be partitioned into two symmetric groups.