Geometric approach to vertex‐degree‐based topological indices–Elliptic Sombor index, theory and application
İvan Gutman, Boris Furtula, Mert Sinan Öz
Abstract
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.
Topics & Concepts
EllipseTopological indexVertex (graph theory)Topology (electrical circuits)Degree (music)MathematicsInterpretation (philosophy)Computer scienceCombinatoricsGeometryPhysicsGraphProgramming languageAcousticsComputational Drug Discovery MethodsGraph theory and applicationsFree Radicals and Antioxidants