In order to evaluate the reliability and fault-tolerant ability of multi-processor system which takes hypercubes as underlying networks, combining the fact that structural faults often occur when the system is invaded by computer viruses, three-length-path structure connectivity and substructure connectivity of the n-cube network were investigated. Firstly, by using the three-length-path structure-cut of the n-cube network, an upper bound of three-length-path structure connectivity of the network was obtained. Secondly, by using an equivalent transformation or a reductive transformation of the three-length-path substructure-set of the n-cube network, a lower bound of three-length-path substructure connectivity of the network was obtained. Finally, combining with the property that three-length-path structure connectivity of a network is not less than its three-length-path substructure connectivity, it was proved that both three-length-path structure connectivity and substructure connectivity of a n-cube network were half of n. The results show that to destroy the enemy's multi-processor system which take the n-cubes as underlying networks under three-length-path structure fault model, at least half of n three-length-path structures or substructures of the system should be attacked.

In view of the disadvantages of small link connectivity, restricted edge connectivity and weak fault tolerance, a kind of augmented bubble-sort network was designed by adding some links to the original bubble-sort network. By constructing a minimum link cut of the n dimensional augmented bubble-sort network, the link connectivity of the n dimensional augmented bubble-sort network was proved to be n, which implied that any two nodes are still connected even deleting n-1 links. The restricted link connectivity of the n dimensional augmented bubble-sort network was proved to be 2 n-2. Therefore, any two nodes of the n dimensional augmented bubble-sort network were still connected even deleting 2 n-3 links if the removal of these links doesn't result in singletons. Based on above results, the example rusults show that the augmented bubble-sort networks is better than bubble-sort network.

In order to measure the fault tolerance ability of the parallel computers which take the k-ary n-cube as underlying topology, by constructing the minimum node set whose removal will lead to every k-ary 1-cube in the k-ary n-cube faulty, a recursive algorithm for finding the k-ary 1-cube subnet preclusion node cut of the k-ary n-cube was proposed. It is proved that at least kn-1 nodes need to be damaged if a rival wants to destroy all k-ary 1-cubes in the k-ary n-cube. The result indicates that there are still undamaged k-ary 1-cubes in the parallel computers which take the k-ary n-cube as underlying topology if the number of the faulty nodes does not exceed kn-1-1.