The Minimal Molecular Tree for the Exponential Randić Index

Topological indices are numerical parameters that provide a way to quantify the structural features of molecules using their graph representations. In chemical graph theory, these indices have been effectively employed to predict various physico-chemical properties of molecules. Among these, the Randić index stands out as a classical and widely used molecular descriptor in chemistry and pharmacology. The Randić index R(G) for a given graph G is defined as R(G)=∑vivj∈E(G)1d(vi)d(vj), where d(vi) represents the degree of vertex vi and E(G) is the set of edges in the graph G. Given the Randić index’s strong discrimination ability in describing molecular structures, a variant known as the exponential Randić index was recently introduced. The exponential Randić index ER(G) for a graph G is defined as ER(G)=∑vivj∈E(G)e1d(vi)d(vj). This paper further explores and fully characterizes the minimal molecular trees in relation to the exponential Randić index. Moreover, the chemical relevance of the exponential Randić index is also investigated.