Fault-tolerant embedding of paths in crossed cubes

The crossed cube CQ(n) is an important variant of the hypercube Q(n) and possesses many desirable properties for interconnection networks. This paper shows that in CQ(n) with f(v) faulty vertices and f(e) faulty edges there exists a fault-free path of length l between any two distinct fault-free vertices for each l satisfying 2(n-1) - 1 <= L <= 2(n) - f(v) - 1 provided that f(v) + f(e) <= n - 3, where the lower bound of l and the upper bound of f(v) + f(e) are tight for some n. Moreover, this result improves the known result that CQn is (n - 3)-Hamiltonian connected. (C) 2008 Elsevier B.V. All rights reserved.