Abstract
The General Sombor index of a graph \( G \) is given by,
\[
SO_\alpha (G) = \sum\limits_{xy\in E(G)} (d_G ^2 (x) + d_G ^2 (y))^\alpha,
\]
where \( d_G (x) \) represents the degree of vertex \( x \) in graph \( G \). This paper focuses on determining the maximum and minimum General Sombor index among trees with given number of pendent vertices, where \( \alpha \in (0,1) \). Additionally, the graphs that achieve the extremal index values are identified and described in this paper.
