Extremal Chemical Trees for a Modified Version of Sombor Index

Let G be a molecular graph, where du representes the degree of vertex u, and uv denotes an edge connecting vertices u and v. A few years ago, a new vertex-degree-based graph invariant (topological index) was introduced by Gutman, defined as SO(G) = ∑ uv∈E √ d²u + d²v, called the Sombor index. Recently, Kulli et al. compared several modified versions of Sombor in dex (Nirmala, Sombor, Dharwad, and F-Sombor indices), they found that these indices are highly correlated and their values for QSPR applications are nearly the same. Based on this study Kulli et al. introduced a new vertex-degree-based topological in dex, which is defined as X(G) = ∑ uv∈E √ d k u + d k v, where k ≥ 1 is a real number. In this paper, we determine the extremal chemical trees with respect to X index.