Graph Theory and Molecular Behavior: Utilizing Platt Numbers and Polynomial Approximations for Boiling Point Estimations

ABSTRACT Analyzing complex multivalued datasets, such as boiling points and molecular Platt numbers, poses significant challenges due to the intricate relationships within the data, which traditional methods struggle to capture effectively. To address this, the study introduces Edge Neighborhood Graphs Ne(G), a novel graph‐based approach where the neighborhoods of edges in a graph G = (V, E) are treated as vertices, and an edge is drawn between two vertices if their corresponding neighborhoods intersect. This method is explored using complete, cycle, and wheel graphs, with formulas derived for vertex degrees in Ne(G) to uncover structural patterns. Polynomial approximations are employed to apply Ne(G) to multivalued data, demonstrating its effectiveness in modeling complex relationships and providing accurate predictions. By offering a powerful new tool for analyzing intricate datasets, this study makes a unique contribution to graph theory and data modeling, with promising potential for application to other graph types and diverse datasets in the future.