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 $EN{T}_{\mathit{ReZ}{G}_1}$ index is the best predictor of boiling point, enthalpy of vaporization, and molar volume, and $EN{T}_{R_{-1}}$ 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.

Reverse entropies are the molecular descriptors that describe the structures of chemical compounds. They are used in isomer discrimination, structure-property relationship, and structure-activity relations. In this study, the QSPR models were designed using the reverse degree-based entropies to predict the physical properties of benzene derivatives. The relationship analyses between the physicochemical properties and the reverse entropies were done by using the curvilinear regression method. A Maple software based algorithm was designed to make the computation of reverse degree-based entropies easy. Analysis was performed using SPSS software. We analyzed that physical properties such as critical pressure, critical temperature, critical volume, Gibb’s energy, LogP, molar refractivity, and Henry’s law can be estimated by the QSPR model using reverse entropies. All the results were highly positive and significant.

Topological indices are quantitative measurements that describe a molecule’s topology and are quantified from the molecule’s graphical representation. The significance of topological indices is linked to their use in QSPR/QSAR modelling as descriptors. Mathematical associations between a particular molecular or biological activity and one or several biochemical and/or molecular structural features are QSPRs (quantitative structure‐property relationships) and QSARs (quantitative structure‐activity relationships). In this paper, we give explicit expressions of two recently defined novel ev‐degree‐ and ve‐degree‐based topological indices of two classes of benzenoid, namely, linear hexagonal chain and hammer‐like benzenoid.

To avoid exorbitant and extensive laboratory experiments, QSPR analysis, based on topological descriptors, is a very constructive statistical approach for analyzing the numerous physical and chemical properties of compounds. Therefore, we presented some new entropy measures which are based on the sum of the neighborhood degree of the vertices. Firstly, we made the partition of the edges of benzene derivatives which are based on the degree sum of neighboring vertices and then computed the neighborhood version of entropies. Secondly, we made use of the software SPSS for developing a correlation between newly introduced entropies and the physicochemical properties of benzene derivatives. Our obtained results demonstrated that the critical temperature , critical pressure , and critical volume can be predicted through fifth geometric arithmetic entropy, second SK entropy, and fifth ND entropy, respectively. Other remaining physical characteristics include Gibb’s energy (qℰ), log(P), molar refractivity (ℳℛ), and Henry’s law (ℋℒ) that can be predicted by using sixth ND entropy.