On the ordering of trees with the general Randic index of the Nordhaus-Gaddum type

The general Randic index of an organic molecule. whose molecular graph is G is defined as the sum of (d(u)d(v))(alpha) over all pairs of adjacent vertices of G, where d(u) is the degree of the vertex u in G and alpha is a real number with alpha not equal 0. In the paper, we obtained sharp bounds on the general Randic index of the Nordhaus-Gaddum type, for trees. Also we. show that the. general Randic. index of the Nordhaus-Gaddum type for double stars S-p,S-q is monotonously increasing in p, where 1 < p <= q.