Computation of degree-dependent topological indices for banana tree graphs

Abstract

A banana tree graph B(n, k) is obtained by connecting one leaf of each of n copies of a k-star graph to a single root vertex that is distinct from all the stars. Due to their branching structure, banana tree graphs resemble certain molecular frameworks and therefore provide a useful mathematical model for studying degree-based topological indices. Such indices, including the Randić index, Zagreb indices, geometric–arithmetic index, and atomic-bond connectivity index, play an important role in chemical graph theory by correlating molecular structure with physicochemical properties. Banana trees also serve as convenient examples for analyzing graph invariants such as diameter, eccentricity, and chromatic number. In this study, we derive closed-form expressions for several degree-based topological indices of banana tree graphs in terms of the parameters n and k. A comparative analysis is carried out to examine the sensitivity of these indices to changes in branching structure. The results highlight how variations in structural parameters influence molecular descriptors, thereby demonstrating the relevance of banana tree graphs in modeling branched molecular systems within chemical graph theory.