The Extremal Unicyclic Graphs With Given Girth for Exponential VDB Topological Indices

Topological indices are widely used molecular structure descriptors in chemistry and pharmaceutics, which help analyze and predict the physicochemical properties and biological activity of compounds. Focusing on the discriminative power, researchers introduced the general exponential VDB topological index, which is defined as follows: . Our current work focuses on studying of some exponential VDB topological indices using general methods. In the paper, we characterize the sufficient conditions for that (1) the graph M n , k is the minimal among unicyclic graph with girth k and (2) the graph H n , k is the maximal among unicyclic graph with girth k , respectively. As an application, the minimal and the maximal unicyclic graphs for some exponential VDB indices are achieved. In addition, we summarize our achievements and propose future research directions in the conclusion.