Fault Diagnosability of Networks With Fault-Free Block at Local Vertex Under MM* Model

In order to evaluate the reliability of a multiprocessor system, the fault diagnosability was introduced and utilized as a significant indicator. In the study of fault diagnosability, researchers usually concentrate on the diagnosability of the global system but ignore its local information. However, the local information also plays a crucial role in the reliability of a multiprocessor system. Thus, an innovative concept of fault diagnosability, called $y$-fault-free-block local fault diagnosability, is put forward to study the fault diagnosability of a multiprocessor system at local vertex, where the $y$-fault-free-block condition requires more than $y$ connected vertices. In this article, we characterize several important properties about the $y$-fault-free-block local fault diagnosability of a multiprocessor interconnection network under the MM* model and propose its $y$-fault-free-block local fault diagnosability at local vertex. Furthermore, we apply our results to some well-known networks, and we obtain their $y$-fault-free-block local fault diagnosabilities at local vertex directly under the MM* model, including bijective connection graph, star graph, and $(n,k)$-star graph. Finally, we compare the $y$-fault-free-block local fault diagnosability of a graph at local vertex with other types of diagnosability, including the diagnosability, conditional diagnosability, good-neighbor diagnosability, and pessimistic diagnosability. It can be seen that the $y$-fault-free-block local fault diagnosability at vertex is larger than all the other types of diagnosability.