Unicyclic graphs with maximum Randić indices

The Randi'c index R(G) of a graph G is the sum of the weights (dudv)−12 of all edges uv in G, where du denotes the degree of vertex u. Du and Zhou [On Randi'c indices of trees, unicyclic graphs, and bicyclic graphs, Int. J. Quantum Chem. 111 (2011), 2760--2770] determined the n-vertex unicyclic graphs with the third for n≥5, the fourth for n≥7 and the fifth for n≥8 maximum Randi'c indices. Recently, Li et al. [The Randi{' c} indices of trees, unicyclic graphs and bicyclic graphs, Ars Combin. 127 (2016), 409--419] obtained the n-vertex unicyclic graphs with the sixth and the seventh for n≥9 and the eighth for n≥10 maximum Randi'c indices. In this paper, we characterize the n-vertex unicyclic graphs with the ninth, the tenth, the eleventh, the twelfth and the thirteenth maximum Randi'c values.