On the Entire Harmonic Index and Entire Harmonic Polynomial of Graphs

A topological descriptor is a numerical parameter that describes a chemical structure using the related molecular graph. Topological descriptors have significance in mathematical chemistry, particularly for studying QSPR and QSAR. In addition, if a topological descriptor has a reciprocal link with a molecular attribute, it is referred to as a topological index. The use of topological indices can help to examine the physicochemical features of chemical compounds because they encode certain attributes of a molecule. The Randić index is a molecular structure descriptor that has several applications in chemistry and medicine. In this paper, we introduce a new version of the Randić index to the inclusion of the intermolecular forces between bonds with atoms, referred to as an entire Harmonic index (EHI), and we present the entire Harmonic polynomial (EHP) of a graph. Specific formulas have been obtained for certain graph classes, and graph operations have been obtained. Bounds and some important results have been found. Furthermore, we demonstrate that the correlation coefficients for the new index lie between 0.909 and 1. In the context of enthalpy of formation and π-electronic energy, the acquired values are significantly higher than those observed for the Harmonic index and the Randić index.