Cancer is one of the most lethal diseases in humans and other species. Breast cancer is the second most frequent cancer after skin cancer, and it develops in the breast. The treatment recommendations are variable. The lack of appropriate medication has worsened the disease. Based on prior research, scientists are testing drugs based on medical therapies. Many drugs which include Abemaciclib, Thiotepa, Anastrozole, Tamoxifen, Abraxane, Capecitabine, Exemestane, and Ixabepilone are listed in the new recommendations. A topological index is a type of molecular descriptor that simply defines numerical values associated with the molecular structure of a compound that is effectively used in modeling many physicochemical properties in numerous quantitative structure-property relationship (QSPR) studies. In this study, several newly defined ve-degree of end vertices of each edge-based entropy indices for breast cancer drugs were investigated. A QSPR was established between entropy indices and the physical properties of breast cancer drugs to assess the efficacy of entropy indices. For the computation of entropy indices, a Maple-based algorithm was developed. The QSPR studies were obtained using the linear and cubic regression methods with the help of SPSS. The obtained results reveal that entropy indices under study have a strong correlation with the physical characteristics. Using simple linear regression, we analyzed that ENTReZG1 index is the best predictor of boiling point, enthalpy of vaporization, and molar volume, and ENTR-1 index is the best predictor of flash point, molar refraction and polarizability. Using cubic regression, we analyzed that the only augmented Zagreb entropy index predicts Melting Point.