The most important application of anticancer drugs in various forms (alkylating agents, hormones agents, and antimetabolites) is the treatment of malignant diseases. Topological indices are widely used in the field of chemical and medical sciences, especially in studying the chemical, biological, clinical, and therapeutic aspects of drugs. In this article, the temperature indices in anticancer drugs molecular graphs such as Carmustine, Convolutamine F, Raloxifene, Tambjamine K, and Pterocellin B were calculated and then analyzed based on physical and chemical properties. The analysis was performed by identifying the best regression models based on temperature indices for six physical and chemical features of anticancer drugs. The results indicated that temperature indices were essential topological indices that predict the properties of anticancer drugs, such as boiling point, flash point, enthalpy, molar refractivity, molar volume, and polarizability. It was also observed that the r value of the regression model was more than 0.6, and the p value was less than 0.05.

Topological indices are numerical values related to a chemical structure that describes the correlation of chemical structure with different physical properties and chemical reactions. Glass has wide applications in architecture, tableware, optics, and optoelectronics. In this article, first, the mathematical relationship between M-polynomial and Banhatti indices such as K-Banhatti, d-Banhatti, and hyper d-Banhatti indices are obtained. Then using M-polynomial, Banhatti indices are calculated.

Graph polynomials based on distance and degree are helpful and necessary because they contain much information about topological indices. In this article, the general inverse sum indeg index and the generalized inverse sum indeg polynomials are calculated for the molecular graph and the line graph of the Titanium dioxide nanotubes. Then, with their help, some polynomials and some degree-based topological indices of the molecular graph and the line graph of Titanium dioxide nanotubes are obtained.

Skin cancer is one of the cancers that in addition to being dangerous, can also affect a person’s self-confidence and beauty. It is caused by the abnormal growth of skin cells. In this article, while providing a closed formula for calculating distance-based indices with the SMP -polynomial approach, the distance indices in the molecular diagram of skin cancer drugs have been calculated and then analyzed based on physical and chemical properties. Our results demonstrate strong correlations between these topological indices and critical physicochemical properties, including polarizability, molar volume, molar refractivity, boiling point, and enthalpy of vaporization. Notably, the vertex Harmonic mean Szeged index exhibited the highest correlation (r=0.981) with polarizability and molar refractivity, underscoring its predictive power. Linear regression models further validated the utility of these indices in drug property prediction, with significant statistical robustness (p<0.05). This work provides a novel mathematical framework for drug design optimization, bridging graph theory with pharmaceutical science. These findings underscore the utility of topological indices in predicting drug-like properties and offer a computationally efficient strategy for the rational design of novel anti-skin cancer agents. The methods presented here bridge graph theory with pharmaceutical science and open avenues for integrating topological descriptors with quantum-chemical calculations in future drug discovery pipelines.