$16$-vertex graphs with automorphism groups $A_{4}$ and $A_{5}$ from icosahedron

Peteris Daugulis

$16$-vertex graphs with automorphism groups $A_{4}$ and $A_{5}$ from icosahedron

Combinatorics 2019-05-02 v1 Group Theory Metric Geometry

Authors: Peteris Daugulis

Abstract

The article deals with the problem of finding vertex-minimal graphs with a given automorphism group. We exhibit two undirected $16$ -vertex graphs having automorphism groups $A_{4}$ and $A_{5}$ . It improves the Babai's bound for $A_{4}$ and the graphical regular representation bound for $A_{5}$ . The graphs are constructed using projectivisation of the vertex-face graph of icosahedron.

Keywords

vertex-minimal graphs automorphism groups icosahedron graph regular representation projectivisation

Cite

@article{arxiv.1905.00212,
  title  = {$16$-vertex graphs with automorphism groups $A_{4}$ and $A_{5}$ from icosahedron},
  author = {Peteris Daugulis},
  journal= {arXiv preprint arXiv:1905.00212},
  year   = {2019}
}

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