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 LTQn is applied widely. In this paper, we show that LTQn is tightly (4n – 9) super 3-extra connected for n ≥ 6 and the 3-extra diagnosability of LTQn under the PMC model and MM* model is 4n - 6 for n ≥ 5 and n ≥ 7, respectively.