  A new geometric background of graph invariants was introduced by Gutman, of
which the simplest is the second Sombor index $SO_2$, defined as
$SO_2=SO_2(G)=\sum_{uv\in E}\frac{|d^2_G(u)-d^2_G(v)|}{d^2_G(u)+d^2_G(v)}$,
where $G = (V, E)$ is a simple graph and $d_G(v)$ denotes the degree of $v$ in
$G$. In this paper, the chemical applicability of the second Sombor index is
investigated and it is shown that the the second Sombor index is useful in
predicting physicochemical properties with high accuracy compared to some
well-established and often used indices. Also, we obtain a bound for the second
Sombor index among all (molecular) trees with fixed numbers of vertices, and
characterize those molecular trees achieving the extremal value.
