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

Published 31 Jul 2022 in math.CO | (2208.00418v1)

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

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