Let G = (V,E) be a locally finite graph, i.e. a graph in which
every vertex has finitely many adjacent vertices. In this paper, we
associate a topology to G, called graphic topology of G and we show
that it is an Alexandroff topology, i.e. a topology in which intersec-
tion of every family of open sets is open. Then we investigate some
properties of this topology. Our motivation is to give an elementary
step toward investigation of some properties of locally finite graphs
by their corresponding topology which we introduce in this paper.