An Alexandroff topology on graphs

Abstract

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