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The Balaban index (also called the  J index) of a connected graph  G is a distance-based topological index, which has been successfully used in various QSAR and QSPR modeling. Although the index was introduced 30 years ago, there are few results on the asymptotic relations. In this paper, several asymptotic bounds on the Balaban indices of trees with diameters 3 and 4 are shown, respectively.

Several Asymptotic Bounds on the Balaban Indices of Trees