The Randić index was one of the most important molecular topological indices, and became a popular topic of research in mathematics and mathematical chemistry. The sharp upper and lower bounds of Randić index of trees, unicyclic graphs and bicyclic graphs have been obtained. Furthermore, the minimal graphs of trees, unicyclic graphs and bicyclic graphs on Randić index have been characterized. In addition, the lower bounds of cacti on Randić index and corresponding extremal graphs have been described. In this paper, we analyzed the degrees of vertices of the edges in cacti, defined the symmetric edges and the asymmetric edges, and characterized some transformations. Based on these definitions, we discussed in terms of maximum degree of vertices. In the end, the extremal graphs have been characterized by the asymmetric edges in cacti of n-vertex given the number of circles with the first, the second, the third, the fourth and the fifth maximum Randić index.
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