Translations and semi-translations in infinite graphs

A self-contraction of an infinite graph is translating if it stabilizes no non-empty finite set of vertices. To each translating self-contractionf of a graph G is associated a particular end ofG, which is called the direction off. This generalizes the concept of direction of a translation (translating automorphism) defined and studied by Halin [5]. In this paper several properties of translating self-contractions are studied, with an emphasis to self-contractions of non-locally finite graphs.