Fault tolerance of (n, k)-Star Graphs

The growing size of a multiprocessor system increases its vulnerability to component failures. As the number of faults in the network structure increases, it is desirable that most of the network stays connected, with at most a few processors separated from the rest, since then the network will continue to be able to function. This paper proved that the largest connected component of the survival graph of (n, k)-Star Graph S_n,k contains almost all the remaining vertices when a lot of faulty vertices occur.