The hamiltonian property of the consecutive-3 digraph

Authors:
G. J. Chang;F. K. Hwang;Li-Da Tong
Affiliations:
Department of Applied Mathematics National Chiao Tung University Hsinchu 30050, Taiwan;Department of Applied Mathematics National Chiao Tung University Hsinchu 30050, Taiwan;Department of Applied Mathematics National Chiao Tung University Hsinchu 30050, Taiwan
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
1997

Citing 6
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Abstract

A consecutive-ifd digraph is a digraph G(d, n, q, r) 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 @? qi + k (mod n) for some k with r @? k @? 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 consecutive-3 digraph is Hamiltonian. This paper produces several infinite classes of consecutive-3 digraphs which are not (respectively, are) Hamiltonian, thus suggesting that the conjecture needs modification.