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Extremal Sombor Index of Chemical trees | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 21 اردیبهشت 1405 اصل مقاله (438.01 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.30867.2745 | ||
| نویسنده | ||
| Hafiza Munam Chand* | ||
| National University of Science and Technology, Islamabad, Pakistan | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Graph Theory؛ Chemical Graph Theory؛ Topological Index؛ degree-based Topological indices؛ Sombor Index | ||
| مراجع | ||
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