Degree-based topological indices and m-polynomial of benzimidazole molecular graph

Chemical graph theory plays an important role in understanding thestructural and physicochemical behaviour of graph-based descriptors. In this work, the hydrogen-suppressed moleculargraph of benzimidazole is investigated using degree-based topological indices and the M-polynomial approach. The molecular structure of benzimidazole is represented as a graph, and the corresponding edge partitions are determined based on the degrees of end vertices. Using these edge partitions, several important degree-based topological indices, namely the First Zagreb index, Second Zagreb index, Randi´c index, Atom-Bond Connectivity index, Geometric-Arithmetic index, Harmonic index, Sum Connectivity index, Hyper Zagreb index, Forgotten index, and Symmetric Division Degree index, are computed systematically. Further, the M-polynomial of the benzimidazole molecular graph is derived and employed to obtain selected topological descriptors. In addition, a simple statistical analysis is performed between selected topological indices and physicochemical properties of benzimidazole using Pearson correlation and linear regression techniques. The correlation coefficient was found to be r ≈ -0.207, indicating a weak negative relationship, while the coefficient of determination was obtained asR^²≈ 0.0428, showing limited predictive capability for the considered dataset. The obtained results provide structural insight into the benzimidazole molecular graph and establish a mathematical basis for future studies involving benzimidazole derivatives and QSPR/QSAR modeling.