Hybrid Fault Diagnosis Capability Analysis of Highly Connected Graphs

Abstract

Abstract 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).