Minimizing the Sombor Index among Trees with Fixed Degree Sequence

Abstract

Vertex-degree-based topological indices have recently gained a lot of attention from mathematical chemists. One such index that we focus on in this paper is called Sombor index. After its definition in late 2020, the Sombor index was quickly recognized as a valuable research topic. In this paper we partially answer the open question of finding the extremal trees with respect to this index for a fixed degree sequence. Particularly we focus on the lower bound and proceed to show that greedy tree minimizes the Sombor index for a given degree sequence.