Robustness of star graph network under link failure

The star graph is an attractive underlying topology for distributed systems. Robustness of the star graph under link failure model is addressed. Specifically, the minimum number of faulty links, f(n, k), that make every (n − k)-dimensional substar S_n−k faulty in an n-dimensional star network S_n, is studied. It is shown that f(n,1)=n+2. Furthermore, an upper bound is given for f(n, 2) with complexity of O(n³) which is an improvement over the straightforward upper bound of O(n⁴) derived in this paper.