### Abstract

Original language | English |
---|---|

Pages (from-to) | 148-180 |

Number of pages | 33 |

Journal | Journal of Combinatorial Theory. Series B |

Volume | 111 |

DOIs | |

Publication status | Published - Mar 2015 |

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### Cite this

*Journal of Combinatorial Theory. Series B*,

*111*, 148-180. https://doi.org/10.1016/j.jctb.2014.10.002

}

*Journal of Combinatorial Theory. Series B*, vol. 111, pp. 148-180. https://doi.org/10.1016/j.jctb.2014.10.002

**Bounding the order of the vertex-stabiliser in 3-valent vertex-transitive and 4-valent arc-transitive graphs.** / Potočnik, P.; Spiga, P.; Verret, Gabriel.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Bounding the order of the vertex-stabiliser in 3-valent vertex-transitive and 4-valent arc-transitive graphs

AU - Potočnik, P.

AU - Spiga, P.

AU - Verret, Gabriel

PY - 2015/3

Y1 - 2015/3

N2 - © 2014 Elsevier Inc. The main result of this paper is that, if Γ is a connected 4-valent G-arc-transitive graph and v is a vertex of Γ, then either Γ is part of a well-understood infinite family of graphs, or |Gv|≤2436 or 2|Gv|log2(|Gv|/2)≤|VΓ| and that this last bound is tight. As a corollary, we get a similar result for 3-valent vertex-transitive graphs.

AB - © 2014 Elsevier Inc. The main result of this paper is that, if Γ is a connected 4-valent G-arc-transitive graph and v is a vertex of Γ, then either Γ is part of a well-understood infinite family of graphs, or |Gv|≤2436 or 2|Gv|log2(|Gv|/2)≤|VΓ| and that this last bound is tight. As a corollary, we get a similar result for 3-valent vertex-transitive graphs.

U2 - 10.1016/j.jctb.2014.10.002

DO - 10.1016/j.jctb.2014.10.002

M3 - Article

VL - 111

SP - 148

EP - 180

JO - Journal of combinatorial Theory Series B

JF - Journal of combinatorial Theory Series B

SN - 0095-8956

ER -