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 H-f(G) = Sigma(u is an element of V(G)) f(deg(G)(u)), where deg(G)(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 zeroth-order general Randic<acute accent> index, sum lordeg index, variable sum exdeg index, Lanzhou index, first and second multiplicative Zagreb indices.