Reliability of DQcube Based on g-Extra Conditional Fault
Hong Zhang, Jixiang Meng
Abstract
Abstract Diagnosability and connectivity are important metrics for the reliability and fault diagnosis capability of interconnection networks, respectively. The g-extra connectivity of a graph G, denoted by $\kappa _g(G)$, is the minimum number of vertices whose deletion will disconnect the network and every remaining component has more than $g$ vertices. The g-extra conditional diagnosability of graph G, denoted by $t_g(G)$, is the maximum number of faulty vertices that the graph G can guarantee to identify under the condition that every fault-free component contains at least g+1 vertices. In this paper, we first determine that g-extra connectivity of DQcube is $\kappa _g(G)=(g+1)(n+1)-\frac{g(g+3)}{2}$ for $0\leq g\leq n-3$ and then show that the g-extra conditional diagnosability of DQcube under the PMC model $(n\geq 4, 1\leq g\leq n-3)$ and the MM$^\ast$ model $(n\geq 7, 1\leq g\leq \frac{n-3}{4})$ is $t_g(G)=(g+1)(n+1)-\frac{g(g+3)}{2}+g$, respectively.