Faulty diagnosability and g-extra connectivity of DQcube. Issue 3 (4th May 2021) - Zhang, Hong; Meng, Jixiang
ABSTRACT: 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 κ 1 ( D Q ( m, d, n ) ) = 2 n and κ 2 ( D Q ( m, d, n ) ) = 3 n − 2 . Second, we determine 1, 2-extra conditional diagnosability and conditional diagnosability of D Q ( m, d, n ) under the PMC model and the MM ∗ model.