Exponential topological indices: optimal inequalities and applications

In this work we obtain inequalities relating a general topological index of a graph, F ( G ) = ∑ u v ∈ E ( G ) f ( d u , d v ) , with its corresponding exponential index, e F ( G ) = ∑ u v ∈ E ( G ) e f ( d u , d v ) when a (symmetric) function f ( · , · ) is evaluated in the degree of the two adjacent vertices to each edge. Besides, we relate two general exponential indices e F 1 and e F 2 that verify a general inequality. These general relations directly yield with new inequalities and bounds involving some well-known topological indices like the generalized atom-bound connectivity index A B C α , the generalized second Zagreb index M 2 α , the generalized Platt index P α , and their corresponding exponential indices e A B C α , e M 2 α , e P α . The results and methodology shown in this work can also be applied to other exponential topological indices. Also, our analysis shows the applicability of the exponential topological indices to the study of several physico-chemical properties of octane isomers.