Degree-based function index of trees and unicyclic graphs

We use functions of two variables satisfying certain conditions to obtain graphs having the smallest value of the degree-based function index among trees and unicyclic graphs with given number of vertices. We show that those extremal results on trees and unicyclic graphs hold for many general degree-based indices such as the general reduced second Zagreb index GRM(a )for a >= 0, general Randi c index R(a )for a > 0, first general Gourava indexFGOafora >= 1, general Z-type index Z(a,b )for a >= 1, b >= -2, general Sombor index SO(a,b )and one other generalization M(a,b )for a >= 1, b > 0. In the study of the maximum value for degree-based indices of trees with given number of vertices, we cover general indices such as SO(a,b )for a > 0, b >= 1, and Z(a,b )for a > 0, b >= -2.