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

TL;DR

This paper determines the maximum Sombor index for trees with a fixed number of vertices and dissociation number, identifying the unique extremal tree for these parameters.

Contribution

It introduces the first characterization of extremal trees with maximum Sombor index given a dissociation number constraint.

Findings

Maximum Sombor index for trees with given dissociation number established

Unique extremal tree identified for each parameter set

Bounds on dissociation number for trees analyzed

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 $\varphi$, where $\ceil*{\frac{2\mathbf{n}}{3}} \leq \varphi(G) \leq \mathbf{n}-1$. We also provide the unique graph among the chosen class where the maximum Sombor index is attained.