The exponent in the general Randic index

We determine conditions for the parameters n and delta, for which the general Randic index R-delta is not an acceptable index of branching of n-vertex trees, i.e., for which the n-vertex star and the n-vertex path have not extremal R(delta-)values among all n-vertex trees. Analogous results are established also in the case of n-vertex chemical trees. Numerous other results for the general Randic index of trees and chemical trees are obtained.