Faulty diagnosability and g-extra connectivity of DQcube

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${}^{\ast }$ model are denoted by $t_g^P\left(G\right)$ and $t_g^M\left(G\right)$, respectively. Due to their many attractive properties, DQcube has received much research interest recently. In this paper, we first determine that ${\kappa }_1\left(DQ\right(m,d,n\left)\right)=2n$ and ${\kappa }_2\left(DQ\right(m,d,n\left)\right)=3n-2$. Second, we determine 1,2-extra conditional diagnosability and conditional diagnosability of $DQ(m,d,n)$ under the PMC model and the MM${}^{\ast }$ model.

Keywords:

• g-extra conditional diagnosability
• g-extra connectivity
• conditional diagnosability
• MM${}^{\ast }$ model
• PMC model

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research is supported by NSFC [grant numbers 11531011]