Following the success of the geometric approach to the Sombor index, Gutman quite recently introduced the elliptic Sombor index, formulated based on the geometric interpretation of ellipses. The elliptic Sombor index is defined as \(\begin{aligned} ESO(G)=\sum _{{uv}\in E(G)} (d_u+d_v)\sqrt{d_{u}^2+d_{v}^2}, \end{aligned}\) where \(d_u\) is the degree of the vertex u in G. Considering the enhanced predictive capability of the reduced Sombor index compared to the Sombor index, we propose a reduced version of the elliptic Sombor index and demonstrate the effectiveness of the elliptic Sombor indices in accurately predicting the physico-chemical properties of octane isomers compared to Sombor indices. In this paper, we determine the extremal values of the elliptic Sombor index of trees with some graphic parameters, including branching number, maximum degree and segment number, along with their complete characterization. Finally, we conclude with our final insights.
