Fault Hamiltonicity and fault Hamiltonian connectivity of the (n, k)-star graphs

In this paper, we consider the fault Hamiltonicity, and the fault Hamiltonian connectivity of the (n, k)-star graph Sn,k. Assume that F V(Sn,k) E(Sn,k). For n k ≥ 2, we prove that Sn,k F is Hamiltonian if F ≤ n 3 and Sn,k F is Hamiltonian connected if F ≤ n 4. For n k 1, Sn,n 1 is isomorphic to the n-star graph Sn which is known to be Hamiltonian if and only if n > 2 and Hamiltonian connected if and only if n 2. Moreover, all the bounds are tight. © 2003 Wiley Periodicals, Inc.