Golden Ratio Bounds for Some Parameters of a Graph

In mathematics, chemistry , and nanoscience a graph model is considered for each molecule, so that the vertices are the atoms of the molecule and the edges are the bonds between the atoms. Graph topological indices are numerical parameters dependent on the graph, which are unique numbers and are fixed with respect to the isomorphism of the graphs. Many topological indices in Mathematical Chemistry are in terms of degrees of vertices. In this article, we study the relationship between some values of these topological indices and the golden ratio.