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 $n$.