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arXiv · 2201.04307

Cubic Graphical Regular Representations of $\mathrm{PSU}_3(q)$

Jing Jian Li·Binzhou Xia·Xiao Qian Zhang·Shasha Zheng
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Abstract

A graphical regular representation (GRR) of a group $G$ is a Cayley graph of $G$ whose full automorphism group is equal to the right regular permutation representation of $G$. Towards a proof of the conjecture that only finitely many finite simple groups have no cubic GRR, this paper shows that $\mathrm{PSU}_3(q)$ has a cubic GRR if and only if $q\geq4$. Moreover, a cubic GRR of $\mathrm{PSU}_3(q)$ is constructed for each of these $q$.

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Jing Jian Li, Binzhou Xia, Xiao Qian Zhang, Shasha Zheng. 2022-01-12. Cubic Graphical Regular Representations of $\mathrm{PSU}_3(q)$. https://arxiv.org/abs/2201.04307

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