On extremal Sombor index of trees with a given independence number $\alpha$
arXiv (Cornell University)(2022)
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 independence number $\alpha$, where $\ceil*{\frac{\mathbf{n}}{2}} \leq \alpha(G) \leq \mathbf{n}-1$. We also provide the unique graph among the chosen class where the maximum Sombor index is attained.
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Key words
extremal sombor index,independence number
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