From a natural generalization to Z2 of the concept of congruence, it is possible to define a family of 2-regular digraphs that we call commutative-step networks. Particular examples of such digraphs are the cartesian product of two directed cycles, C1 x Ch, and the fixed-step network (or 2-step circulant digraph) DN,a,b.
In this paper the theory of congruences in Z2 is applied to derive three equivalent characterizations of those commutative-step networks that have a Hamiltonian cycle. Some known results are then obtained as a corollary. For instance, necessary and sufficient conditions for C1 x Ch or DN,a,b to be hamiltonian are discussed.
@article{urn:eudml:doc:38993,
title = {Ciclos de Hamilton en redes de paso conmutativo y de paso fijo.},
journal = {Stochastica},
volume = {12},
year = {1988},
pages = {113-129},
zbl = {0689.05028},
mrnumber = {MR1024753},
language = {es},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38993}
}
Fiol Mora, Miguel Angel; Andrés Yebra, José Luis. Ciclos de Hamilton en redes de paso conmutativo y de paso fijo.. Stochastica, Tome 12 (1988) pp. 113-129. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38993/