Conditional Fault-Tolerant Cycle-Embedding of Crossed Cube

The crossed cube, which is a variation of the hypercube, possesses some properties superior to the hypercube. In this paper, assuming that each node is incident with at least two fault-free links, we show that an n-dimensional crossed cube can tolerate up to 2n - 5 link faults, while retaining a fault-free Hamiltonian cycle. The result is optimal with respect to the number of link faults tolerated. We also verify that the assumption is practically meaningful by evaluating its probability to occur, which is very close to 1, even if n is small