Based on medical experiments, the molecular structure of drugs includes information about their physical-chemical properties. A theoretical descriptor tool for assessing these features is known as a topological index. In this study, the molecular structure of two anticancer drugs hyaluronic acid-Paclitaxel/Curcumin conjugates using an edge-division strategy in graph theory are evaluated. To ensure the correctness of calculations in this study, we use Mathematica and Matlab software. Several new invariants based on the vertex degree are computed for the molecular structures of ayaluronic acid conjugated with curcumin and paclitaxel. We obtain the exact values of these topological indices. The calculation of topological indices for these anticancer drugs provides a more comprehensive understanding of their molecular properties and biological behavior.