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PreprintCC BY 4.0arXiv

Vertex-transitive strongly regular graphs in the switching class of doubly transitive two-graphs

  • Robert F. Bailey
  • Gábor P. Nagy
  • Valentino Smaldore
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Abstract

Let G be a permutation group that acts $2$-transitively on the finite set V and let 𝒯=(V,T) be a two-graph whose automorphism group contains G. In this paper, we classify those strongly regular graphs Γ with vertex set V whose automorphism group is a transitive maximal subgroup of G and whose associated two-graph is 𝒯. In doing so, we obtain a new family of vertex-transitive strongly regular graphs whose associated two-graph arises from PΣL(2,q).

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Cite

BibTeXRIS
BibTeX
@misc{bailey2026vertextransitive,
  title = {{Vertex-transitive strongly regular graphs in the switching class of doubly transitive two-graphs}},
  author = {Robert F. Bailey and Gábor P. Nagy and Valentino Smaldore},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.30330},
  eprint = {2608.30330},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.30330},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Vertex-transitive strongly regular graphs in the switching class of doubly transitive two-graphs
AU  - Robert F. Bailey
AU  - Gábor P. Nagy
AU  - Valentino Smaldore
PY  - 2026
DA  - 2026/08/31
PB  - arXiv
DO  - 10.48550/arxiv.2608.30330
UR  - https://arxiv.org/abs/2608.30330
AB  - Let G be a permutation group that acts $2$-transitively on the finite set V and let 𝒯=(V,T) be a two-graph whose automorphism group contains G. In this paper, we classify those strongly regular graphs Γ with vertex set V whose automorphism group is a transitive maximal subgroup of G and whose associated two-graph is 𝒯. In doing so, we obtain a new family of vertex-transitive strongly regular graphs whose associated two-graph arises from PΣL(2,q).
ER  -