On the Ordering of Trees with the General Randić Index of the Nordhaus-Gaddum Type ∗

The general Randić index of an organic molecule whose molecular graph is G is defined as the sum of (d(u)d(v)) α over all pairs of adjacent vertices of G, where d(u) is the degree of the vertex u in G and α is a real number with α � = 0. In the paper, we obtained sharp bounds on the general Randić index of the Nordhaus-Gaddum type for trees. Also we show that the general Randić index of the Nordhaus-Gaddum type for double stars Sp,q is monotonously increasing in p, where 1 < p ≤ q. 1