The g-extra connectivity and diagnosability of crossed cubes.

Connectivity and diagnosability are two important parameters for the fault tolerant of an interconnection network G. In 1996, Fàbrega and Fiol proposed the g-extra connectivity of G. In 2016, Zhang et al. proposed the g-extra diagnosability of G that requires every component of G−S has at least (g+1) vertices. The g-extra connectivity of G is necessary for g-extra diagnosability of G. In this paper, we show that the g-extra connectivity of the crossed cube CQn is n(g+1)−12g(g+3) for n ≥ 5, 0≤g≤⌊n2⌋ and the g-extra diagnosability of CQn is (n−12g)(g+1) under the PMC model for n ≥ 5, 0≤g≤⌊n2⌋ and the MM* model for n ≥ 7, 0≤g≤⌊n2⌋.