A study of fault tolerance in star graph

The bounds on f(n,k), the number of faulty nodes to make every (n−k)-dimensional substar Sn−k in an n-dimensional star network Sn, have been derived. The exact value for f(n,k) is determined when n is prime and k=2, or when n−2?k?n. For 2<k<n−2, a general method is presented to derive a set of faulty nodes which damage all Sn−k's in Sn.