On the Extremal General Sombor Index of Trees with Given Pendent Vertices

Abstract

The General Sombor index of a graph G is given by,where dG(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 α ∈ (0, 1). Additionally, the graphs that achieve the extremal index values are identified and described in this paper.