A note on path embedding in crossed cubes with faulty vertices

摘要

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 2(n) 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 <= 2(n) - vertical bar F vertical bar - 1. In this note, we show that, for crossed cubes CQ(n) with n >= 5, the range of l can be extended to [2n - 5, 2(n) - vertical bar F vertical bar - 1. Moreover, we also show that the vertices of CQ(5) can be partitioned into two symmetric groups. (C) 2017 Elsevier B.V. All rights reserved.