Construction of an Alexandroff topology on the edge set of an undirected graph

Abstract

In this paper, we introduce a new topology T^E_G on the edge set of an undirected graph G=(V,E) named E-graphic topology. We will study some properties of this topology in particular we prove that T^E_G is an Alexandroff topology. In addition, we investigate the compactness, connectedness and relation with functions between graphs. Finally, we give some characterization of homeomorphism between two E-graphic topologies.