Best lower and upper bounds for the Randić index R − 1 of chemical trees ∗

The general Randić index Rα(G) of a graph G is defined as the sum of the weights (d(u)d(v)) α of all edges uv of G, where d(u) denotes the degree of a vertex u in G and α is an arbitrary real number. Clark and Moon gave the lower and upper bounds for the Randić 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.