Independent (Non-Adjacent Vertices) Topological Spaces Associated with Undirected Graphs, With Some Applications in Biomathematices

Abstract

In this work, we associate a new topology to undirected graph G = (V, E) which may contain one isolated vertex or more and we named it Independent (non-adjacent vertices) Topology. A new sub-basis family to generate the Independent Topology is introduced on the set of n vertices V and for every vertex v of V the number of adjacent vertices is not greater than n − 2 (In simple graph we can say : for every vertex v of V, Δ(G) = n − 2, where Δ(G) is the maximum degree of vertices in a graph G). Then we give a fundamental step toward investigation of some properties of undirected graphs by their corresponding Independent Topology which we introduce in this work. Furthermore, an application to our new model (Independent Topology) are presented, that to carry out a framework in practical life like biomathematics (applied examples in biomathematics).