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arXiv · 2208.00418

On the general Sombor index of unicyclic graphs with a given diameter

Xipeng Hu·Lingping Zhong
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Abstract

The general Sombor index of $G$ is defined as $SO_α(G)= \sum_{uv\in G}\left(d^2_{G}(u)+d^2_{G}(v)\right)^α$. For $0<α<1$, we have the upper bound of $SO_α(G)$ on unicyclic graphs with a fixed diameter, and the extremal graph is also characterized.

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Xipeng Hu, Lingping Zhong. 2022-07-31. On the general Sombor index of unicyclic graphs with a given diameter. https://arxiv.org/abs/2208.00418

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