DECOMPOSING ENDS OF LOCALLY FINITE GRAPHS

An important invariant of translations of infinite locally finite grap hs is that of a direction as introduced by HALIN. This invariant gives not much information if the translation is not a proper one. A new re fined concept of directions is investigated. A double ray D of a graph X is said to be metric, if the distance metrics in D and X on V(D) ar e equivalent. It is called geodesic, if these metrics are equal. The t ranslations leaving some metric double ray invariant are characterized . Using a result of POLAT and WATKINS, we characterize the translation s leaving some geodesic double ray invariant.