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PreprintarXiv licencearXiv

Prime-valent Symmetric Cayley Graphs of Characteristically Simple Groups

  • Feng Deng
  • Jing Jian Li
  • Hao Yu
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Abstract

Let Ga be a connected prime-valent X-arc-transitive Cayley graph of a finite characteristically simple group G≅ Tk, where kgeqslant2. We obtain a precise structural characterization of such graphs and their arc-transitive automorphism groups. In the cubic case, every connected symmetric Cayley graph of Tk, where T is a finite nonabelian simple group, is normal.

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Cite

BibTeXRIS
BibTeX
@misc{deng2026primevalent,
  title = {{Prime-valent Symmetric Cayley Graphs of Characteristically Simple Groups}},
  author = {Feng Deng and Jing Jian Li and Hao Yu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.27582},
  eprint = {2609.27582},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.27582},
}
RIS
TY  - UNPB
TI  - Prime-valent Symmetric Cayley Graphs of Characteristically Simple Groups
AU  - Feng Deng
AU  - Jing Jian Li
AU  - Hao Yu
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.27582
UR  - https://arxiv.org/abs/2609.27582
AB  - Let Ga be a connected prime-valent X-arc-transitive Cayley graph of a finite characteristically simple group G≅ T^k, where kgeqslant2. We obtain a precise structural characterization of such graphs and their arc-transitive automorphism groups. In the cubic case, every connected symmetric Cayley graph of T^k, where T is a finite nonabelian simple group, is normal.
ER  -