Non-Incidence (Non-End Vertices) Topological Spaces Associated With Simple Graphs

Abstract

Let G = (V,E) be a simple graph. In this paper, we associate a topology to G, called non-incidence (non-end vertices of the edge ) topology of G. A sub-basis family to generate the non-incidence topology is introduced on the set of vertices V. Then we investigate some properties and discuss the non-incidence topology on a certain few important types of graphs. Our motivation is to give an fundamental step toward investigation of some properties of simple graphs by their corresponding non-incidence topology which we introduce in this paper. 2010 Mathematics Subject Classification: 05C99, 54A05.