Fuzzy topological structures via fuzzy graphs and their applications

Fuzzy graphs are an individual of application tools in the area of mathematics, which permit the users to define the relative between concepts because the wildlife of fuzziness is satisfactory for any situation. They are helpful to give more exactness and suppleness to the classification as associated with the traditional models. A topological structure is a set model for graphs. The main purpose of this paper is to introduce a new kind of fuzzy topological structures in terms of fuzzy graphs called fuzzy topological graphs due to a class of fuzzy subsets, and some of their properties are investigated. Also, a new procedure to calculate the number of edges in fuzzy graphs will be defined. Further, we consider the concept of a homeomorphic between fuzzy topological graphs as a fuzzy topological property that can be used to prove the isomorphic between fuzzy graphs. Moreover, an algorithm based on the proposed operations that build some fuzzy topological graphs will be presented. Finally, we give a new method to explain the homeomorphic between some fuzzy topological graphs which will be applied in smart cities.