Fault diameter and fault tolerance of HCN(n,n)

We provide the way to make an n+1 node disjoint parallel path between any two nodes of HCN(n,n) which has a better network cost than the hypercube, and prove that the fault diameter of HCN(n,n) is dia(HCN(n,n))+4 by result. These parallel paths can reduce the time of transmitting messages between nodes, and they mean that if some nodes of HCN(n,n) would fail, there is still no communication delay time. Also, by analyzing the fault tolerance of the interconnection network HCN(n,n), we prove that there is maximal fault tolerance.