Sombor indices–back to geometry

The Sombor index ( S O ) is a vertex-degree-based graph invariant, defined as the sum over all pairs of adjacent vertices of √ d 2 i + d 2 j , where d i is the degree of the i -th vertex. It has been conceived using geometric considerations. Numerous researches of S O that followed, ignored its geometric origin. We now show that geometry-based reasonings reveal the geometric background of several classical topological indices (Zagreb, Albertson) and lead to a series of new S O -like degree-based graph invariants.