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.