The t/kt/k-diagnosability and hh-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 κh(G) be the h-extra connectivity of G. Then, we can deduce that G is κh(G)/h-diagnosable under the PMC model with some basic conditions. All κh(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 κh(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：

---

通过额外连接实现大规模互联网络的悲观故障诊断能力


t/kt/k-可诊断性和hh-额外连通性被视为提高网络可靠性的两个重要指标。 t/k诊断策略可以显着提高网络的自诊断能力，但代价是不超过k个无故障节点被误诊断为故障。 h-额外连接可以通过确保每个剩余组件具有不少于 h+1 个节点来极大地提高网络的实际容错能力。然而，关于这两个指标之间的内在关系的研究却很少。在本文中，我们调查了（Liu，2020）中导致严重缺陷结果的原因，并提出了一种诊断算法，通过考虑 PMC 模型下的大规模连通网络 G 的 t/k-可诊断性h-额外的连接性。设κh(G)为G的h-额外连通性。那么，在满足一些基本条件的PMC模型下，我们可以推论G是κh(G)/h-可诊断的。在大规模连通网络G中，所有κh(G)个故障节点都能被正确诊断，最多有h个无故障节点被误诊为故障。完整的容错方法采用组合属性和线性多次故障分析来攻克我们证明的核心。我们将应用新发现的关系直接获得一系列众所周知的网络的κh(G)/h-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、由转置树、冒泡排序星形图、交替组图、分裂星形网络、k 元 n 立方体和 (n,k) 星形图。