On fault tolerance of (n,k)-star networks

Abstract

Fault tolerance of an $(n,k)$-star network is measured by its $h$-super connectivity ${\kappa }_s^{(h)}$ or $h$-super edge-connectivity ${\lambda }_s^{(h)}$. Li {\it et al.} [Appl. Math. Comput. 248 (2014), 525-530; Math. Sci. Lett. 1 (2012), 133-138] determined ${\kappa }_s^{(h)}$ and ${\lambda }_s^{(h)}$ for $0\le h\le n-k$. This paper determines ${\kappa }_s^{(h)}={\lambda }_s^{(h)}=\frac{(h+1)!(n-h-1)}{(n-k)!}$ for $n-k\le h\le n-2$.