Extremal vertex-degree function index of trees with some given parameters

For a graph G, the vertex-degree function index of G is defined as Hf (G) = ?u?V(G) f(degG(u)), where degG(u) stands for the degree of vertex u in G and f(x) is a function defined on positive real numbers. In this article, we determine the extremal values of the vertex-degree function index of trees with given number of pendent vertices/segments/branching vertices/maximum degree vertices and with a perfect matching when f(x) is strictly convex (resp. concave). Moreover, we use the results directly to some famous topological indices which belong to the type of vertex-degree function index, such as the zerothorder general Randic index, sum lordeg index, variable sum exdeg index, Lanzhou index, first and second multiplicative Zagreb indices.