Hybrid Fault Diagnosis Capability Analysis of Highly Connected Graphs

Zhu et al. introduced the h-edge tolerable diagnosability to measure the fault diagnosis capability of a multiprocessor system with faulty links This kind of diagnosability is a generalization of the concept of traditional diagnosability. A graph is called a maximally connected graph if its minimum degree equals its vertex connectivity. It is well-known that many irregular networks are maximally connected graphs and the h-edge tolerable diagnosabilities of these networks are unknown, which is our motivation for research. In this paper, we obtain the lower bound of the h-edge tolerable diagnosability of a class of t-connected graphs and establish the h-edge tolerable diagnosability of a class of maximally connected graphs under the PMC model and the MM * model, which extend some results in (Hakimi, S.L. and Amin, A.T. (1974) Characterization of connection assignment of diagnosable systems. IEEE Trans. Comput., 23, 86-88), (Chang, C.P., Lai, P.L., Tan, J.J.M. and Hsu, L.H. (2004) Diagnosability of t-connected networks and product networks under the comparison diagnosis model. IEEE Trans. Comput., 53, 1582-1590) and (Lian, G., Zhou, S., Hsieh, S.Y., Liu, J., Chen, G. and Wang, Y. (2019) Performance evaluation on hybrid fault diagnosability of regular networks. Theoret. Comput. Sci., 796, 147-153).