Any graph that depicts a particular molecular structure can be given a topological graph index, also known as a molecular descriptor. From this index, it is possible to examine numerical data and learn more about some of the physical characteristics of a molecule. In this study, we construct and explore a novel variation for graphs termed the exponential Wiener index (EW(G)) and the multiplicative exponential Wiener index \(\prod EW(G)\) . Typical graphs for which it is also conceivable include the wheel graph, fan graph, star graph, full graph, cycle graph, complete graph, and complete bipartite graph. Additionally, some EW(G) bounds are determined using exponential inequalities. In the end, an algorithm is created to obtain EW(G), and the most effective is investigated. This work is also extended to the molecular graphs for n-alkanes, n = 1,2,..., 10 and benzenoid hydrocarbons. Additionally, a QSPR study that takes into account the molecular mass, melting point, and boiling point of alkanes and total \(\pi\) -electronic energy \(\left( E_\pi \right)\) , enthalpy of formation \(\left( \Delta _f^0\right)\) , and boiling points have been conducted. The influential measures such as DFBETAS, DFFITS, Hadi’s measure, are calculated by which the influential parameters and the outliers are identified for the regression models between the topological index and these physical parameters.
