Geometric Approach to Vertex-Degree-based Topological Indices-Elliptic Sombor Index, Theory and Application

A novel geometric method is proposed for constructing vertex-degree-based molecular structure descriptors (topological indices). The model is based on an ellipse whose focal points represent the degrees of a pair of adjacent vertices. This approach enables a geometric interpretation of several previously known topological indices, and lead to design of a few new. The area of the ellipse induces a vertex-degree-based topological index of remarkable simplicity, which we call elliptic Sombor index(ESO$$ ESO $$). The main mathematical properties of ESO$$ ESO $$ are established, especially its relations to other, earlier known, indices. Then the applicative potential of ESO$$ ESO $$ is analyzed. The elliptic Sombor index (ESO) is a topological molecular descriptor derived from the geometric properties of an ellipse. It is defined by using the equation of the area of an ellipse. image