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Let $d_v$ be the degree of the vertex $v$ in a connected graph $G$. The firstBanhatti-Sombor index of $G$ is defined as $BSO(G) =\sum_{uv\inE(G)}\sqrt{\frac{1}{d^2_u}+\frac{1}{d^2_v}}$, which is a newvertex-degree-based topological index introduced by Kulli. In this paper, themathematical relations between the first Banhatti-Sombor index and some otherwell-known vertex-degree-based topological indices are established. Inaddition, the trees extremal with respect to the first Banhatti-Sombor index ontrees and chemical trees are characterized, respectively.

On the first Banhatti-Sombor index