Faulty diagnosability and g-extra connectivity of DQcube
Hong Zhang, Jixiang Meng · International Journal of Parallel Emergent and Distributed Systems · 2020
Fault diagnosis of systems is an important area of study in the design and maintenance of multiprocessor systems. In 2005, Lai et al. proposed a new measure for the fault diagnosis of systems, namely, conditional diagnosability, which requires that all the neighbours of any processor in a multiprocessor system cannot be faulty at the same time. In 2017, Zhang et al. proposed a new measure for the fault diagnosis of systems, namely, g-extra conditional diagnosability, which requires that every component of G−F has more than g vertices in the system. The g-extra conditional diagnosabilty of a graph G under the PMC model and the MM∗ model are denoted by tgP(G) and tgM(G), respectively. Due to their many attractive properties, DQcube has received much research interest recently. In this paper, we first determine that κ1(DQ(m,d,n))=2n and κ2(DQ(m,d,n))=3n−2. Second, we determine 1,2-extra conditional diagnosability and conditional diagnosability of DQ(m,d,n) under the PMC model and the MM∗ model.