Geometric Approach to Degree-Based Topological Index: Hyperbolic Sombor Index

This article presents a new geometric approach to forming molecular structure descriptors (topological indices) based on vertex degrees. The degrees of a pair of adjacent vertices are represented by the length of the semi-major and semi-minor axes of the hyperbola that form the basis of the model. In this way, a number of previously known topological indices can now be interpreted geometrically and some new topological indices can be generated. The eccentricity of the hyperbola gives rise to a remarkably simple vertex-degree-based topological index, which we refer to as the hyperbolic Sombor index (HSO). We concentrate on some of the most important properties of this index, such as prediction power, structure sensitivity and degeneracy. We apply statistical approaches and computing methods to the octane, nonane and decane isomer data sets to compare these properties with other well-known degree-based topological indices.