Sombor index of trees with at most three branch vertices

摘要

Let G be a graph with set of vertices V(G) and set of edges  E(G). The Sombor index is a vertex-degree-based-topological index recently introduced by Ivan Gutman, defined asSO(G)=∑uv∈E(G)(du)2+(dv)2.In this paper we determine the extremal values of SO over trees with at most three branch vertices.