Fault Free Rings and Linear Arraies Embedded in the Faulty (n, k)-star Networks

Abstract

In this paper, we consider the embedding of hamimilton cycle and the hamil- tonian paths between any two vertices of the (n, k)-star graph Sn,k. Assume that F V (Sn,k) [ E(Sn,k). For n-k2, we prove that Sn,k-F is hamiltonian if jFj n3 and Sn,kF is hamiltonian connected if jFj n4. For nk = 1, Sn,n1 is isomorphic to the star graph Sn and it is known that Sn is hamiltonian if and only if n > 2 and Sn is hamiltonian connected if and only if n = 2. Moreover, all the bounds are tight.