Abstract
The crossed cube C Q n is an important variant of the hypercube Q n and possesses many desirable properties for interconnection networks. This paper shows that in C Q 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 C Q n is ( n − 3 ) -Hamiltonian connected.
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