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arXiv · 2609.27613

On Arc-Transitive Regular Covers of Cubic Edge-Primitive Graphs

Feng Deng·Jing Jian Li·Yu Wang·Hao Yu
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Abstract

We determine, up to isomorphism of the covering graphs, the connected arc-transitive regular covers of cubic edge-primitive graphs whose covering transformation group is cyclic or elementary abelian of order $p^2$, where $p$ is a prime. Combining the known classifications for the base graphs ${\rm K_{3,3}}$ and ${\rm DC_{14}}$ with new arguments for ${\rm F30A}$ and ${\rm F102A}$ gives the full list in these two classes of covering groups. In the cyclic case, the covers of ${\rm F30A}$ and ${\rm F102A}$ are ${\rm F90A}$ and ${\rm F204A}$, respectively. In the elementary abelian case, neither ${\rm F30A}$ nor ${\rm F102A}$ admits an arc-transitive regular $\mathbb{Z}_p^2$-cover, so the base graph is ${\rm K_{3,3}}$ or ${\rm DC_{14}}$.

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Feng Deng, Jing Jian Li, Yu Wang, Hao Yu. 2026-09-23. On Arc-Transitive Regular Covers of Cubic Edge-Primitive Graphs. https://arxiv.org/abs/2609.27613

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