Previous research has shown a substantial correlation between a chemical compound’s molecular structure and its chemical characteristics. Understanding the physical characteristics and biological functions of biomolecules can be improved with the aid of topological indices based on their molecular structure. Eccentricity-connectivity indices, which describe molecular structures based on distance, have been applied to the mathematical modelling of a wide range of biological activities. In this article, we compute the exact formulae of various versions of the eccentricity-connectivity index for first type of Dominating David-derived network. The findings can be applied to computer-aided molecular design methods in pharmaceutical engineering.