Fault-tolerant Hamiltonian laceability of balanced hypercubes

The balanced hypercube, as a new variant of hypercube, has many desirable properties such as strong connectivity, high regularity and symmetry. The particular property of the balanced hypercube is that each processor has a backup processor sharing the same neighborhood. A Hamiltonian bipartite graph G = ( V 0 ? V 1 , E ) is said to be Hamiltonian laceable if there is a Hamiltonian path between any two vertices x ? V 0 and y ? V 1 . It has been proved that the balanced hypercube BH n is Hamiltonian laceable for all n ? 1 . In this paper, we have proved that after at most 2 n - 2 faulty edges occur, BH n remains Hamiltonian laceable for all n ? 2 , this result is optimal with respect to the number of faulty edges can be tolerated in BH n .

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