Best lower and upper bounds for the Randic index R1 of chemical trees

The general Randic index R(G) of a graph G is dened as the sum of the weights (d(u)d(v)) of all edges uv of G, where d(u) denotes the degree of a vertex u in G and is an arbitrary real number. Clark and Moon gave the lower and upper bounds for the Randic index R 1 of all trees, and posed the problem to determine better bounds. In this paper we give the best possible lower and upper bounds for R 1 among all chemical trees, i.e., trees with maximum degree at most 4. Some (but not all) of the corresponding tree structures are also determined.