Fuzzy topological invariants in uniform fuzzy graphs

Abstract

 In this paper, we have defined some fuzzy topological invariants for particular types of uniform fuzzy graph. Some particular useful types of uniform fuzzy graphs are Uniform Edge Fuzzy Graph, Uniform Vertex Fuzzy Graph, Uniform Vertex-Edge Fuzzy Graph and Totally Uniform Fuzzy Graph. For each particular type we have defined different kinds of degrees in a graph in accordance with the unique nature of it. In the end, we have applied all our output results to a cellular neural fuzzy graph as an example, to verify the predicting ability of topological invariants. The aim of this paper is to define more significant fuzzy topological invariants in fuzzy graphs. Our ideas will help to create a link between fuzzy graph theory and simple (crisp) graph theory.