The Hamiltonian Property of the Consecutive-3 Digraph
نویسندگان
چکیده
A consecutive-d digraph is a digraph G(d, n, q, T) whose n nodes are labeled by the residues modulo n and a link from node i to node j exists if and only if j I pi + k (mod n) for some k with r 5 k 5 r + d 1. Consecutive-d digraphs are used as models for many computer networks and multiprocessor systems, in which the existence of a Hamiltonian circuit is important. Conditions for a consecutive-d graph to have a Hamiltonian circuit were known except for gcd(n, d) = 1 and d = 3 or 4. It was conjectured by Du, Hsu, and Hwang that a consecutivo3 digraph ls Hamiltonian. This paper produces several infinite classes of consecutive-3 digraphs which are not (respectively, are) Hamiltonian, thus suggesting that the conjecture needs modification. Keywords-Hamiltonian circuit, Consecutive-d digraph, Network, Loop.
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