On extremal Sombor index of trees with a given dissociation number $\phi$

Abstract

The Sombor index is a topological index in graph theory defined by Gutman in 2021. In this article, we find the maximum Sombor index of trees of order $\mathbf{n}$ with a given dissociation number $\phi$, where $\ceil*{\frac{2\mathbf{n}}{3}} \leq φ(G) \leq \mathbf{n}-1$. We also provide the unique graph among the chosen class where the maximum Sombor index is attained.