Let G be a simple graph and d(u) the degree of its vertex u. The Sombor index (SO) and the degree-ratio Sombor index (DRSO) of G are vertex-degree-based (VDB) graph invariants, equal to the sum over all pairs of adjacent vertices u, v of G, of the terms \(\sqrt{d(u)^2+d(v)^2}\) and \(\sqrt{[d(u)/d(v)]^2 + [d(v)/d(u)]^2}\) , respectively. Thus, DRSO is obtained from SO when d(u) is replaced by d(u)/d(v) and when d(v) is replaced by d(v)/d(u). This transformation, denoted by \({\hat{\mathcal{R}}}\) , can be applied to other VDB graph invariants (topological indices). In this paper, we examine the \({\hat{\mathcal{R}}}\) -transformations of the class of best known VDB topological indices, and show that in most cases the result is an index from the same class. Moreover, in remarkably many cases the \({\hat{\mathcal{R}}}\) -transform is an irregularity measure.
