Hamiltonian Connectedness of the Faulty WK-Recursive Network

Authors:
Jung-Sheng Fu
Affiliations:
National United University, Taiwan
Venue:
PDCAT '06 Proceedings of the Seventh International Conference on Parallel and Distributed Computing, Applications and Technologies
Year:
2006

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Abstract

Much research on the WK-recursive network has been published during the past few years due to its many favorable properties. We use K(d, t) 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 \geqslant 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|d \leqslant - 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.