Extra (component) connectivity and diagnosability of bubble sort networks

As generalizations of traditional connectivity (resp., diagnosability), h-component connectivity (resp., diagnosability) and h-extra connectivity (resp., diagnosability) are significant parameters to characterize invulnerability of multiprocessor systems. In this paper, we determine that h-extra connectivity of bubble sort networks B-n is k(h) (B-n) = (h +1)(n - 1) - h(h+3)/2 for 0 <= h <= n/2. Afterwards, we show that h-extra diagnosability of B-n under PMC model and MM* model is t(h) (B-n) = (h+1) (n- 1) - h(h+3)/2 + h. In addition, we show that (h + 1)-component connectivity of B-n is cK(h+1)(Bn) = h(n - 1) - h(h+1)/2 + 1, and h-component diagnosability of B-n under PMC model and MM* model is ct(h) (B-n) = h(n - 1) - h(h + 1)/2 + 1 for 1 <= h <= n/2.