Local-connectivity on FQn with a large number of faulty nodes

The n-dimensional folded hypercube FQ_n is an important variance of the hypercube Q_n. It has many attractive properties and has received many researchers´ extensive attention. In this paper, we discuss two kinds of local-connectivity based on the folded hypercube network FQ_n: local k-sub-folded-hypercube-connectivity and local sub-folded-hypercube-connectivity. Each k-sub-folded-hypercube FQ_k contains less than 2^k-1 faulty nodes in a local k-sub-folded-hypercube-connectivity FQ_n, and all the non-faulty nodes in FQ_k make a connected graph. For each k-sub-folded-hypercube FQ_k of FQ_n, where k ≥ 1, there is an h-dimensional sub-folded-hypercube FQ_h containing FQ_k(thus h ≥ k) such that FQ_h is local h-sub-folded-hypercube connected in a local sub-folded-hypercube-connectivity FQ_n. We lead two theorems by the definition of local connectivity and show that a locally connected FQ_n with a large number of faulty nodes is also globally connected. By the results of this paper, the fault tolerant capability of FQ_n is improved greatly.