Sombor, Nirmala, Dharwad, and F-Sombor Indices – A Comparative Study

Abstract

Let G be a molecular graph, d(u) the degree (number of first neighbors) of its vertex u, and uv its edge connecting the vertices u and v. In the recent literature, four vertex-degree-based molecular structure descriptors have been put forward, named Nirmala, Sombor, Dharwad, and F-Sombor indices, equal to the sum of the terms \( \sqrt{d(u)^k + d(v)^k} \) over all edges uv of G for k=1,2,3, and 4. In this work, we compare these four indices. We find that they are highly correlated, and their value for QSPR applications is nearly the same. Therefore, only one (any one) of these topological indices should be used. From an applicative point of view, there was no need to introduce and study them separately.