Diagnosability of the strong product of paths and cycles under PMC Model

Graphs are suitable for modeling interconnection networks when designing parallel computing systems such as multiprocessor systems. Multiprocessor systems can significantly increase computational speed and efficiency by distributing tasks among multiple processors and allowing them to work simultaneously. If some processors fail, it can indeed have a significant impact on the parallel processing capability of a multiprocessor system. Therefore, the diagnosability serves as a crucial parameter. It is unquestionable that an outstanding multiprocessor system exhibits robust fault diagnosis capability. Investigating the system's interconnection network to determine its diagnosability is an essential step in designing highly reliable multiprocessor systems. In this paper, we construct a large network obtained by the strong product of paths and cycles, which is beneficial for a parallel computing system. We subsequently determine its diagnosability to be 5 under the PMC model. Additionally, it has some good properties and is suitable for designing multiprocessor systems.