Local diagnosability of generic star-pyramid graph

The problem of fault diagnosis in network has been discussed widely. In this paper, we study the local diagnosability of a generic star-pyramid graph. We prove that under the PMC model the local diagnosability of each vertex in a generic star-pyramid graph is equal to its degree and the generic star-pyramid has the strong local diagnosability property. Then we study the local diagnosability of a faulty graph. After showing some properties of the graph, we prove that a generic star-pyramid graph keeps the strong property no matter how many edges are faulty under the condition that each vertex is incident with at least four fault-free edges.