On Ve-Degree and Ev-Degree Topological Properties of Hyaluronic Acid‐Anticancer Drug Conjugates with QSPR

Abstract

The design of the quantitative structure-property/activity relationships for drug-related compounds using theoretical methods relies on appropriate molecular structure representations. The molecular structure of a compound comprises all the information required to determine its chemical, biological, and physical properties. These properties can be assessed by employing a graph theoretical descriptor tool widely known as topological indices. Generalization of descriptors may reduce not only the number of molecular graph-based descriptors but also improve existing results and provide a better correlation to several molecular properties. Recently introduced ve-degree and ev-degree topological indices have been successfully employed for development of models for the prediction of various biological activities/properties. In this article, we propose the general ve-inverse sum indeg index ${\text{ISI}}_{\left(\alpha ,\beta \right)}^{\text{ve}}\left(G\right)$ and general ve-Zagreb index $M_{\alpha }^{\text{ve}}\left(G\right)$ of graph $G$ and compute ${\text{ISI}}_{\left(\alpha ,\beta \right)}^{\text{ve}}\left(G\right),M_{\alpha }^{\text{ve}}\left(G\right)$ , and $M_{\alpha }^{\text{ev}}\left(G\right)$ (general ev-degree index) of hyaluronic acid-curcumin/paclitaxel conjugates, renowned for its potential anti-inflammatory, antioxidant, and anticancer properties, by using molecular structure analysis and edge partitioning technique. Several ve-degree- and ev-degree-based topological indices are obtained as a special case of ${\text{ISI}}_{\left(\alpha ,\beta \right)}^{\text{ve}}\left(G\right),M_{\alpha }^{\text{ve}}\left(G\right)$ , and $M_{\alpha }^{\text{ev}}\left(G\right)$ . Furthermore, QSPR analysis of ${\text{ISI}}_{\left(\alpha ,\beta \right)}^{\text{ve}}\left(G\right),M_{\alpha }^{\text{ve}}\left(G\right)$ , and $M_{\alpha }^{\text{ev}}\left(G\right)$ for particular values of $\alpha$ and $\beta$ is performed, which reveals their predicting power. These results allow researchers to better understand the physicochemical properties and pharmacological characteristics of these conjugates.