The tightly super 3-extra connectivity and diagnosability of locally twisted cubes

Diagnosability of a multiprocessor system G is one important measure of the reliability of interconnection networks. In 2016, Zhang et al. proposed the g-extra diagnosability of G, which restrains that every component of G - S has at least (g + 1) vertices. The locally twisted cube LTQ_n is applied widely. In this paper, we show that LTQ_n is tightly (4n-9) super 3-extra connected for n≥6 and the 3-extra diagnosability of LTQ_n under the PMC model and MM* model is 4n - 6 for n≥5 and n≥7, respectively.