The study of the topological indices in the quantitative structure–activity and structure–property models are used to predict the physicochemical properties of the chemical compounds. In this paper, we analyze the molecular structure of hyaluronic acid conjugated with methotrexate which is used in anticancer drugs. We obtain the exact formulas for several new Sombor‐type vertex‐degree‐based topological indices and the Banhatti–Sombor‐type vertex‐degree‐based topological indices of the molecular structure of hyaluronic acid–methotrexate conjugate using the graph theory and the edge‐partition approach. We use Matlab and Mathematica software to evaluate the results and accuracy of calculations. The numerical results in this study can help understand the biological activity of the chemical structure of these drugs.