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Automorphism groups of Cayley graphs on almost simple groups with normal connection sets

  • Mengyu Cao
  • Benjian Lv
  • Binzhou Xia
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Abstract

We determine the full automorphism group of every connected Cayley graph on an almost simple group with a normal connection set. We also characterize exactly when the full automorphism group is generated by right translations, group automorphisms preserving the connection set, and inversion. Our results substantially generalize several results in the literature, including the known determinations of the automorphism groups of derangement graphs, complete transposition graphs and complete alternating group graphs. As a further application, we establish criteria for a finite nonabelian simple group to admit a graphical doubly regular representation and determine exactly which alternating groups do so, correcting claims in the literature.

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Cite

BibTeXRIS
BibTeX
@misc{cao2026automorphism,
  title = {{Automorphism groups of Cayley graphs on almost simple groups with normal connection sets}},
  author = {Mengyu Cao and Benjian Lv and Binzhou Xia},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.21679},
  eprint = {2609.21679},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.21679},
}
RIS
TY  - UNPB
TI  - Automorphism groups of Cayley graphs on almost simple groups with normal connection sets
AU  - Mengyu Cao
AU  - Benjian Lv
AU  - Binzhou Xia
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2609.21679
UR  - https://arxiv.org/abs/2609.21679
AB  - We determine the full automorphism group of every connected Cayley graph on an almost simple group with a normal connection set. We also characterize exactly when the full automorphism group is generated by right translations, group automorphisms preserving the connection set, and inversion. Our results substantially generalize several results in the literature, including the known determinations of the automorphism groups of derangement graphs, complete transposition graphs and complete alternating group graphs. As a further application, we establish criteria for a finite nonabelian simple group to admit a graphical doubly regular representation and determine exactly which alternating groups do so, correcting claims in the literature.
ER  -