Geometric approach to vertex‐degree‐based topological indices–Elliptic Sombor index, theory and application

Abstract 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 (). The main mathematical properties of are established, especially its relations to other, earlier known, indices. Then the applicative potential of is analyzed.