Ring embedding in faulty (n,k)-star graphs

In this paper we consider the ring embedding problem in faulty (n,k)-star graphs. An (n,k)-star graph is recently proposed as an attractive interconnection network topology and also known as the generalized version of an n-star graph with scalability such that the number of nodes in the graph can be suitably adjustable by two dimensioning parameters n and k. Our scheme is proceeded in top-down style in such a manner that the resulting sub-stars maintain evenly distributed faults. We show that a ring of length n!/(n-k)!-f can be found in an (n,k)-star graph having n!/(n-k)! nodes when the number of faulty nodes f is at most n-3 and n-k⩾2