Reliability of DQcube Based on g-Extra Conditional Fault

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) - g(g+3)/2 for 0 <= g <= n - 3 and then show that the g-extra conditional diagnosability of DQcube under the PMC model (n >= 4, 1 <= g <= n - 3) and the MM* model (n >= 7, 1 <= g <= n-3/4) is t(g)(G) = (g + 1)(n + 1) - g(g+3)/2 + g, respectively.

Automated summary

This paper investigates the connectivity and conditional diagnosability of DQcube network, providing mathematical formulas for them and analyzing and comparing them under different models.