On the Exponential Atom-Bond Connectivity Index of Graphs

Several topological indices are possibly the most widely applied graph-based molecular structure descriptors in chemistry and pharmacology. The capacity of topological indices to discriminate is a crucial component of their study. In light of this, the literature has introduced the exponential vertex-degree-based topological index. The exponential atom-bond connectivity index is defined as follows: (Formula presented.) where (Formula presented.) is the degree of the vertex (Formula presented.) in (Formula presented.). In this paper, we prove that the double star (Formula presented.) is the second maximal graph with respect to the (Formula presented.) index of trees of order n. We give an upper bound on (Formula presented.) of unicyclic graphs of order n and characterize the maximal graphs. The graph (Formula presented.) gives the maximal graph with respect to the (Formula presented.) index of bicyclic graphs of order n. We present several relations between (Formula presented.) and (Formula presented.) of graph (Formula presented.). Finally, we provide a conclusion summarizing our findings and discuss potential directions for future research.