New types of graphs induced by topological spaces

In this article, a technique to construct a new type of topological structures by graphs called topological graphs is introduced. We use the concept of a homeomorphism between topological graphs as a topological property to prove the isomorphic between graphs. We construct a computer program that builds graphs and its topological graphs. This model helps in studying many topological properties such as continuity, connectedness, compactness and separation axioms on graphs. Finally, we present some examples of different types of graphs and their topological graphs and study some of their topological and algebraic properties.