# QSPR analysis of anticancer drugs using the Euler–Sombor index and theoretical insights on its minimum value for unicyclic graphs

## TL;DR

This paper explores a new mathematical tool to predict properties of anticancer drugs based on their molecular structure.

## Contribution

The study introduces the Euler–Sombor index for QSPR modeling and extends theoretical results on unicyclic graphs.

## Key findings

- The Euler–Sombor index correlates significantly with properties like boiling point and melting point of anticancer drugs.
- The study characterizes unicyclic graphs with the third minimum Euler–Sombor index.

## Abstract

Topological indices (TIs) are powerful tools for exploring the relationship between molecular structure and drug activity, offering a cost-effective alternative to experimental screening. The Euler–Sombor index, a recently introduced degree-based TI, captures key structural features of molecules that influence their physico-chemical behaviour. This study investigates the use of the Euler–Sombor index in quantitative structure–property relationship (QSPR) modeling of anticancer drugs. By applying linear, quadratic, and logarithmic regression models, we predict important properties such as boiling point (BP), melting point (MP), enthalpy (E), and molar refraction (MR). The results show a significant correlation between the Euler–Sombor index and these molecular properties. In addition, we extend the result of Su and Tang by characterizing unicyclic graphs that have the third minimum Euler–Sombor index.