Geometric Approach to Degree-Based Topological Indices: Degree-Ratio Sombor Indices of Graphs

An alternative geometric interpretation of vertex-degree-based topological indices is introduced.Let (d(u), d(v)) denote the degree pair of the edge uv E(G) andits corresponding degree-ratio pair.Based on the Euclidean metric, a novel class of graph invariants is considered, of which the simplest member is a Degree-Ratio Sombor index DRSO.The DRSO index is obtained by summing the termsFundamental mathematical properties of the DRSO index are established.Several structural variants of the DRSO index, including the modified and reduced versions, are formulated.