The diagnosability of triangle-free graphs

The ability of identifying all the faulty devices in a multiprocessor system is known as diagnosability. The local diagnosability concerns the local connective substructure in a network. The PMC model is the test-based diagnosis with a processor performing the diagnosis by testing the neighboring processors via the links between them. In this paper, we discuss the diagnosability and the local diagnosability of a triangle-free network under the PMC model. We also propose the local diagnosis algorithms under the PMC model for some specific structures.