Faulty diagnosability andg-extra connectivity of DQcube

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 t(g)(P)(G) and t(g)(M) (G), respectively. Due to their many attractive properties, DQcube has received much research interest recently. In this paper, we first determine that kappa(1)(DQ(m, d, n)) = 2n and kappa(2)(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.

Automated summary

The paper discusses fault diagnosis measures for multiprocessor systems proposed by Lai et al. and Zhang et al. in 2005 and 2017 respectively. The study focuses on the g-extra conditional diagnosability of graphs under different models and also examines the conditional diagnosability of DQ(m, d, n) systems. Additionally, the research determines the values of kappa(1)(DQ(m, d, n)) and kappa(2)(DQ(m, d, n)).