Hamiltonian Connectedness of the Faulty WK-Recursive Network

Much research on the WK-recursive network has been published during the past few years due to its many favorable properties. We use K(d1t) to denote a WK-recursive network of level t, each of whose basic modules is a d-node complete graph, where d <> 1 and t ges 1. Let F denote the set of faulty nodes in K(d, t). In this study, we show that K(d, t) - F is Hamiltonian connected when | F| les d - 4. Therefore, K(d, t) - F can embed the longest linear array between any two distinct nodes with dilation, congestion, load, and expansion all equal to one. In addition, since the connectivity of K(d, t) is d - 1, the result is optimal