Investigation molecular structure of anticancer drug with topological indices

Abstract

A crucial consideration in examining the physicochemical characteristics of chemical compound structures is topological indices. In addition, topological indices will serve as a description of a molecule under test by translating each molecule’s structure into a real number. In this paper, we calculate topological indices $T_{(\alpha ,\beta )}\left(G\right)={\sum }_{ab\in E\left(G\right)}{\left(d_a^{\alpha }+d_b^{\alpha }\right)}^{\beta }$ and $mS{O}_{\alpha }\left(G\right)={\sum }_{ab\in E\left(G\right)}{\left(\frac{d_a^{\alpha }+d_b^{\alpha }}{2}\right)}^{1/\alpha }$ for anticancer drugs, where $d_a$ is the degree of vertex $a$ in graph $G$ and $0\ne \alpha ,\beta \in R$. By choosing of parameters $\alpha$ and $\beta$, some of new/old results for topological indices are obtained. The results of this study may assist to chemists in identifying the chemical, physical and biological activity associated with them.