Multiplicative topological indices: Analytical properties and application to random networks

We consider two general classes of multiplicative degree-based topological indices (MTIs), denoted by X pi,FV(G) = {u is an element of V(G) FV(du) and X pi,FE(G) = pi uv is an element of E(G) FE(du, dv), where uv indicates the edge of G connecting the vertices u and v, du is the degree of the vertex u, and FV(x) and FE(x, y) are functions of the vertex degrees. This work has three objectives: First, we follow an analytical approach to deal with a classical topic in the study of topological indices: to find inequalities that relate two analysis of MTIs as a generic tool for studying average properties of random networks, extending analysis of MTIs which allows us to state a scaling law that relates different random graph models.