ABSTRACT Chemical graph theory acts as a tool for converting molecular information to a numerical parameter. Topological indices are numeric quantities that are related to the physio-chemical properties of chemical compounds. Distance- and Degree-based topological indices and Counting-related polynomials are three prominent and extensively researched classes of topological indices. In all these categories, distance-based topological descriptors have a significant impact on chemical graph theory. In this paper, the ‘Total eccentricity index ζ ( G ) , the Geometric-arithmetic index G A 4 ( G ) , Eccentricity-based Zagreb indices M 1 ∗ ( G ) , M 1 ∗ ∗ ( G ) and M 2 ∗ ( G ) , the Average eccentricity index a v e c ( G ) and the Atom-bond connectivity index A B C 5 ( G ) ’ of hexagonal networks are computed.