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

The Sombor index of a hypergraph H defined by SO(H)=∑_eᵢ ∈ E√∑_u ∈ eᵢdH(u)², where dH(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).