The Sombor index for $k$-uniform hypertrees with given number of segments

The Sombor index of a hypergraph $H$ defined by $SO(H)=\sum\limits_{e_{i} \in E}\sqrt{\sum\limits_{u \in e_{i}}d_{H}(u)^{2}},$ where $d_{H}(u)$ is the degree of the vertex $u$ of $H$. Motivated by earlier work of Shetty and Bhat, we define some new hypergraph operations and give the structural characteristics of connected $k$-uniform hypertrees. Based on these results, we determine the maximum (minimum) value of the Sombor index of connected $k$-uniform hypertrees with given number of segments and characterize the corresponding extremal hypertrees. This generalizes the results of Chen et al. (2022).