The Edge-fault Tolerant Hamiltonian of the Balanced Hypercube

Huang and Wu proposed a new network which is called balanced hypercube, the balanced hypercube is a variant of the hypercube network. As a crucial factor to evaluate the performance of the interconnection networks, fault tolerance of the interconnection networks has been widely studied in recent years. Hence, it is nature to consider the fault tolerance of the balanced hypercubes. Wu and Huang have proved that the balanced hypercube is bipartite graph. Hao has proved that there exists a fault-free Hamiltonian path between any two adjacent vertices in BHn with (2n- 2) faulty edges. This paper has proved one Hamiltonian property in BHn with (n - 1) faulty edges.