On the ordering of the Randić index of unicyclic and bicyclic graphs

Let $d_x$ be the degree of the vertex $x$ in a graph $G$. The Randić index of $G$ is defined by $R(G) = \sum_{xy \in E(G)} (d_x d_y)^ {-\frac{1}{2}}$. Recently, Hasni et al. [Unicyclic graphs with Maximum Randi\'{c} indices, Communication in Combinatorics and Optimization, 1 (2023), 161--172] obtained the ninth to thirteenth maximum Randić indices among the unicyclic graphs with $n$ vertices. In this paper, we correct the ordering of Randić index of unicyclic graphs. In addition, we present the ordering of maximum Randi\'c index among bicyclic graphs of order $n$.