The properties and t/s-diagnosability of k-ary n-cube networks

An increase in network system size increases the risk of node failure in a system. To maintain the reliability of the system, the faulty nodes need to be repaired or replaced with additional nodes, which implies that the approach of locating the faulty nodes in the system is a research topic of great significance. There are various kinds of diagnosis strategies, such as the t-diagnosis strategy, t/s-diagnosis strategy, t/t-diagnosis strategy and t/k-diagnosis strategy. When we use the t/s-diagnosis strategy to identify faulty nodes, some fault-free nodes may be identified as faulty nodes. In addition, the choice of the specific diagnosis model to identify faulty nodes is important; the Preparata, Metze and Chen (PMC) model is widely used. In this paper, we study the t/s-diagnosability of the k-ary n-cube under the PMC model. First, we obtain several structural properties of k-ary n-cubes. Then, we use these properties and determine that the 3-ary n-cube is $$\eta /\eta +h-1$$ -diagnosable, where $$n\geqslant 2$$ , $$1\leqslant h\leqslant n-1$$ and $$2hn-3(h-1)-\frac{(h-1)(h-2)}{2}-1<\eta \leqslant 2(h+1)n-3h-\frac{h(h-1)}{2}-1$$ , and that the k-ary n-cube is $$\eta /\eta +h-1$$ -diagnosable, where $$k\geqslant 4$$ , $$n\geqslant 2$$ , $${1\leqslant h\leqslant n-1}$$ and $$2hn-2(h-1)-\frac{(h-1)(h-2)}{2}-1<\eta \leqslant 2(h+1)n-2h-\frac{h(h-1)}{2}-1$$ .