Exponential Vertex–Degree–Based Topological Indices and Discrimination (2019)
We discuss the discrimination property of vertex–degree–based (VDB) topological indices over Gn, the set of graphs with n non-isolated vertices. Concretely, we consider a partition of Gn into equivalence classes induced by an equivalence relation on Gn. Then we say that a VDB topological index has the discrimination property with respect to an equivalence relation on Gn if it discriminates equivalence classes. This is a generalization of the usual concept of discrimination in topological indices. If ϕ is a VDB topological index, then we introduce the mb ϕ-structure relation on Gn and show that the exponential of the best known VDB topological indices have the discrimination property. In view of the nice mathematical properties e ϕ has, we study extremal values of Randić’s exponential index over Gn.