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On Arc-Transitive Regular Covers of Cubic Edge-Primitive Graphs
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 p2, where p is a prime. Combining the known classifications for the base graphs K3,3 and DC14 with new arguments for F30A and F102A gives the full list in these two classes of covering groups. In the cyclic case, the covers of F30A and F102A are F90A and F204A, respectively. In the elementary abelian case, neither F30A nor F102A admits an arc-transitive regular ℤp2-cover, so the base graph is K3,3 or DC14.
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BibTeX
@misc{deng2026arctransitive,
title = {{On Arc-Transitive Regular Covers of Cubic Edge-Primitive Graphs}},
author = {Feng Deng and Jing Jian Li and Yu Wang and Hao Yu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27613},
eprint = {2609.27613},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27613},
}
RIS
TY - UNPB
TI - On Arc-Transitive Regular Covers of Cubic Edge-Primitive Graphs
AU - Feng Deng
AU - Jing Jian Li
AU - Yu Wang
AU - Hao Yu
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.27613
UR - https://arxiv.org/abs/2609.27613
AB - 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 K_3,3 and DC_14 with new arguments for F30A and F102A gives the full list in these two classes of covering groups. In the cyclic case, the covers of F30A and F102A are F90A and F204A, respectively. In the elementary abelian case, neither F30A nor F102A admits an arc-transitive regular ℤ_p^2-cover, so the base graph is K_3,3 or DC_14.
ER -