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.

中文翻译：

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基于g-额外条件故障的DQcube的可靠性

可诊断性和连通性分别是互连网络的可靠性和故障诊断能力的重要指标。图G的g额外连通性由| $ \ kappa _g（G）$ |⁠表示，是其删除将断开网络连接且所有其余分量均大于| $ g $ |的最小顶点数。顶点。图G的g额外条件可诊断性，用| $ t_g（G）$ |⁠表示，是图G在每个无故障分量至少包含g的条件下可以保证识别的最大故障顶点数。 +1个顶点。在本文中，我们首先确定DQcube的g额外连通性是| $ \ kappa _g（G）=（g + 1）（n + 1）-\ frac {g（g + 3）} {2} $ | 对于| $ 0 \ leq g \ leq n-3 $ | 然后证明在PMC模型| $（n \ geq 4，1 \ leq g \ leq n-3）$ |下DQcube的g附加条件可诊断性 和MM | $ ^ \ ast $ | 模型| $（n \ geq 7，1 \ leq g \ leq \ frac {n-3} {4}）$ | 分别为| $ t_g（G）=（g + 1）（n + 1）-\ frac {g（g + 3）} {2} + g $ |⁠。