The h-Extra Connectivity and Diagnosability of Locally Twisted Cubes

The connectivity and diagnosability of a system or a network are two important measures. In 1996, Fabrega and Fiol proposed the h-extra connectivity of the network G = (V, E), which is necessary for (h, m)-diagnosability of networks. In 2016, Zhang et al. proposed the (h, m)-diagnosability of G that requires every component of G - S has at least (h + 1) nodes for S subset of V. The locally twisted cube LTQ(n) is applied widely. There are many studies on LTQn. In this paper, we show that the h - extra connectivity of LTQ(n) is n - 1/2h(h - 2n + 3) for n >= 5 and 0 <= h <= n - 3, and m of the (h, m)- diagnosability of LTQ(n) is n - 1/2h(h - 2 n + 1) for n >= 5, 0 <= h <= n - 3 in the PMC model and n >= 7, 0 <= h <= n - 3 in the MM* model, respectively.