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

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Abstract

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.

Keywords

Valency 3
Valency 4
Vertex-transitive
Arc-transitive
Locally-dihedral

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Also affiliated with: UP FAMNIT, University of Primorska, Glagoljaška 8, 6000 Koper, Slovenia.