The $t/k$t/k-diagnosability and $h$h-extra connectivity are regarded as two important indicators to improve the network reliability. The $t/k$ -diagnosis strategy can significantly improve the self-diagnosing capability of a network at the expense of no more than $k$ fault-free nodes being mistakenly diagnosed as faulty. The $h$ -extra connectivity can tremendously improve the real fault tolerability of a network by insuring that each remaining component has no fewer than $h+1$ nodes. However, there is few result on the inherent relationship between these two indicators. In this article, we investigate the reason that caused the serious flawed results in (Liu, 2020), and we propose a diagnosis algorithm to establish the $t/k$ -diagnosability for a large-scale connected network $G$ under the PMC model by considering its $h$ -extra connectivity. Let $\kappa _h(G)$ be the $h$ -extra connectivity of $G$ . Then, we can deduce that $G$ is $\kappa _h(G)/h$ -diagnosable under the PMC model with some basic conditions. All $\kappa _h(G)$ faulty nodes can be correctly diagnosed in the large-scale connected network $G$ and at most $h$ fault-free nodes would be misdiagnosed as faulty. The complete fault tolerant method adopts combinatorial properties and linearly many fault analysis to conquer the core of our proofs. We will apply the newly found relationship to directly obtain the $\kappa _h(G)/h$ -diagnosability of a series of well known networks, including hypercubes, folded hypercubes, balanced hypercubes, dual-cubes, BC graphs, star graphs, Cayley graphs generated by transposition trees, bubble-sort star graphs, alternating group graphs, split-star networks, $k$ -ary $n$ -cubes and $(n,k)$ -star graphs.

中文翻译：

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通过额外连接的大规模连接网络的悲观故障诊断

这 $t/k$吨/克- 可诊断性和$h$H-额外的连通性被认为是提高网络可靠性的两个重要指标。这$t/k$ -诊断策略可以显着提高网络的自诊断能力，代价不超过 $千$无故障节点被误诊为故障。这$h$ - 额外的连通性可以通过确保每个剩余组件的数量不少于 $h+1$节点。然而，关于这两个指标之间的内在关系的结果很少。在本文中，我们调查了导致 (Liu, 2020) 中严重缺陷结果的原因，并提出了一种诊断算法来建立$t/k$ - 大规模连接网络的可诊断性 $G$ 在 PMC 模型下，通过考虑其 $h$ - 额外的连接。让$\kappa _h(G)$ 成为 $h$ - 额外的连接 $G$ . 那么，我们可以推断出$G$ 是 $\kappa_h(G)/h$ -在具有一些基本条件的PMC模型下可诊断。全部$\kappa _h(G)$ 在大规模连接的网络中可以正确诊断故障节点 $G$ 并且至多 $h$无故障节点将被误诊为故障。完全容错方法采用组合特性和线性多故障分析来征服我们证明的核心。我们将应用新发现的关系直接获得$\kappa_h(G)/h$ -一系列众所周知的网络的可诊断性，包括超立方体、折叠超立方体、平衡超立方体、双立方体、BC图、星图、转置树生成的凯莱图、冒泡排序星图、交替群图、分裂星网络, $千$ -ary $n$ - 立方体和 $(n,k)$ -星图。