Study of eccentricity based topological indices for benzenoid structure

Topological indices play paramount role in defining chemical and structural properties of different compounds. Chemical graph theory is useful for predicting the bioactivity and physicochemical properties through numerical invariants. A broad range of topological indices are studied and used in theoretical chemistry. The eccentricity of a graph is maximum distance from one vertex a to another vertex b. The connectivity based topological indices depict vital role in mathematical chemistry. In this paper, we discuss Benzenoid Hourglass Network and calculate its total eccentricity, average eccentricity, atom-bond connectivity index, eccentricity based Zagreb index and geometric-arithmetic index. Some new helpful closed formulas are developed