Conditional fault tolerance properties of (n, k)-star graphs

Conditional connectivity and conditional fault diameter have been proposed as two important parameters in estimating the fault tolerance property of interconnection networks. In this paper, we consider the conditional fault tolerance properties of (n, k)-star graphs through investigating the conditional connectivity and conditional fault diameter. We show that under the conditional fault assumption, where all neighbors of any vertex cannot be faulty simultaneously, the (n, k)-star graph S
n, k
can tolerate up to n + k − 4 faulty vertexes. We also prove that in the worst case, the fault diameter is increased by 6 over the fault-free diameter.