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As an important topological index, the fifth geometric-arithmetic index is used to test the chemical properties of chemical compounds, nanomaterials and drugs. In this paper, by means of graph structure analysis and edge dividing technology, the formulate for calculating the fifth geometric-arithmetic index of bridge graph is given. Furthermore, we present the fifth geometric-arithmetic index of carbon nanocones CNCn(k).
Gao et al. (Mon,) studied this question.