Conjugated trees with minimum general Randić index

The general Randić index Rα(G)Rα(G) is the sum of the weights (dG(u)dG(v))α(dG(u)dG(v))α over all edges uvuv of a (molecular) graph GG, where αα is a real number and dG(u)dG(u) is the degree of the vertex uu of GG. In this paper, for any real number α≤−1α≤−1, the minimum general Randić index Rα(T)Rα(T) among all the conjugated trees (trees with a Kekulé structure) is determined and the corresponding extremal conjugated trees are characterized. These trees are also extremal over all the conjugated chemical trees.