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[in Journal: Journal of Interconnection Networks] AND [Keyword: Sombor Index] (1)	27 Mar 2025	Run
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articleNo Access
On Sombor Index of Unicyclic and Bicyclic Graphs
- Huan Tan and
- Biao Zhao
Journal of Interconnection Networks23 Jul 2024
Preview Abstract
Gutman proposed a topological index called the Sombor index, which was defined as
$S O (G) = \sum u v \in E (G) \sqrt{{(d_{G} (u))}_{G}^{2} + {(d_{G} (v))}_{G}^{2}},$ $S O (G) = \sum_{u v \in E (G)} \sqrt{{(d_{G} (u))}^{2} + {(d_{G} (v))}^{2}},$
where $d_{G} (v)$ is the degree of the vertex $v$ in graph $G$ . In this paper, we determine the second-minimum and second-maximum values of the Sombor index over all the unicyclic graphs of order $n (n \geq 5)$ and bicyclic graphs of order $n (n \geq 6)$ .

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