Structure Connectivity and Substructure Connectivity of (n, k)-Star Graph Networks

The (n, k)-star graph S_n, k is a generalization of the star graph. The structure connectivity and substructure connectivity are two generalizations of the classical connectivity, which can be used to measure the fault tolerance of the network whose faults must be some subgraphs with a special structure. In this paper, we will determined the structure connectivity and substructure connectivity of (n, k)-star graphs with respect to the complete graph structures.