elliptic sombor index of chemical graphs

Let $g$ be a simple graph. the elliptic sombor index of $g$ is defined as $$    eso(g) = sum_{uv} left(d_{u}+ d_{v} right)sqrt{d^{2}_{u}+d^{2}_{v}},$$  where $d_{u}$ denotes the degree of the vertex $u$, and the sum runs over the set of edges of $g$. in this paper we solve the extremal value problem of $eso$ over the set of (connected) chemical graphs and over the set of chemical trees, with equal number of vertices.