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arXiv · 2501.08747

Every group is the automorphism group of a graph with arbitrarily large genus

Marco Barbieri
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Abstract

We prove that, to every abstract group $G$, we can associate a sequence of graphs $\Gamma_n$ such that the automorphism group of $\Gamma_n$ is isomorphic to $G$ and the genus of $\Gamma_n$ is an unbounded function of $n$.

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Marco Barbieri. 2025-01-15. Every group is the automorphism group of a graph with arbitrarily large genus. https://arxiv.org/abs/2501.08747

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