The Relations Between the Wings and the Ends of the Infinite Graphs

Abstract:

      The wing and the end are two important concepts of the infinite graph. They play a key role in the path decomposition theory.It is a interesting prob-lem to find the relations between the wings and the ends of a infinite graph. The settlement of the problem will integerate many results about the path dec decomposition theory of the infinite graphs. But so far,I haven't seen any re result for the problem. In this paper I solve the problem thoroughly. As a app lication of these results,! show that C.ST. J . A.Nash-williams theorem is equivalent to B.Zelinka's theorem.