Extremal Sombor Index of Chemical trees

Articles in Press

Document Type : Original paper

Author

National University of Science and Technology, Islamabad, Pakistan

Abstract

A novel invariant based on vertex degree was recently proposed by Gutman, called the Sombor index, and defined as
  \begin{equation*}
  \mathcal{SO}(\mathcal{G})=\sum_{v_{1}v_{2}\in \mathcal{E}(\mathcal{G})}\sqrt{\text{d}(v_{1})^2+\text{d}(v_{2})^2},\end{equation*}
where $ \text{d}(v_{1}) $ is the degree of vertex $v_{1}$ in $G$.  This paper investigates the extremal values of the Sombor index of chemical trees with exactly one vertex of degree $4$. We characterize the tree attaining the maximum value of the Sombor index and provide the expression for their Sombor indices. Furthermore, we identify the minimum trees and demonstrate that these yield unique tree structures. These results contribute to the structural understanding of degree-based invariants in chemical graph theory.

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References

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Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 11 May 2026

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