Fault-tolerant ring embedding in star graphs

We consider an injured star graph with some faulty links and nodes. We show that even with f_e⩽n-3 faulty links a Hamiltonian cycle still can be found in an n-star, and that with f_v ⩽n-3 faulty nodes a ring containing at most 4f_v nodes less than that in a Hamiltonian cycle can be found (i.e., containing at least n!-4f_v nodes). In general, in an n-star with f_e faulty links and f_v faulty nodes, where f _e+f_v⩽n-3 our embedding is able to establish a ring containing at least n!-4f_v nodes