Topological Structure of Nonwandering Set of a Graph Map

Let G be a graph (i.e., a finite onedimensional polyhedron) and f : G G be a continuous map. In this paper, we show that every isolated recurrent point of f is an isolated nonwandering point; every accumulation point of the set of nonwandering points of f with infinite orbit is a twoorder accumulation point of the set of recurrent points of f; the derived set of an limit set of f is equal to the derived set of an the set of recurrent points of f; and the twoorder derived set of nonwandering set of f is equal to the twoorder derived set of the set of recurrent points of f.