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arXiv · 2108.10384

Smallest graphs with given automorphism group

Danai Deligeorgaki
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Abstract

For a finite group $G$, denote by $\alpha(G)$ the minimum number of vertices of any graph $\Gamma$ having $\text{Aut}(\Gamma)\cong G$. In this paper, we prove that $\alpha(G)\leq |G|$, with specified exceptions. The exceptions include four infinite families of groups, and 17 other small groups. Additionally, we compute $\alpha(G)$ for the groups $G$ such that $\alpha(G)> |G|$ where the value $\alpha(G)$ was previously unknown.

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Danai Deligeorgaki. 2021-08-23. Smallest graphs with given automorphism group. https://arxiv.org/abs/2108.10384

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