Abstract
The harmonic index of a graph G is denoted by H(G) and is defined as H(G) = Sigma(uv is an element of E(G)) 2/d(u)+d(v), where d(u), d(v) denote the degrees of the vertices u, v, respectively, of G and E(G) is the edge set of G. In this paper, the graphs having sixth to fifteenth maximum harmonic indices are characterized from the class of all n-vertex trees for sufficiently large n.