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

2010/10/12 by Primož Potočnik, Pablo Spiga, Potocnik, Primoz +3 · 5 citations
Computer Science · Mathematics · #Advanced Graph Theory Research #Advanced Operator Algebra Research #Combinatorics (math.CO) #Cooperative Communication and Network Coding #FOS: Mathematics #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.1010.2546

openalex publication_date 2010/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The main result of this paper is that, if \Γ is a connected 4-valent\nG-arc-transitive graph and v is a vertex of \Γ, then either \Γ\nis one of a well understood infinite family of graphs, or |G_v|\≤ 2⁴3⁶ or\n2|G_v|\log₂(|G_v|/2)\≤ | V\Γ| and that this last bound is tight. As a\ncorollary, we get a similar result for 3-valent vertex-transitive graphs.\n

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