The smallest vertex-primitive 2-arc-transitive digraph

2022/06/13 by Fu‐Gang Yin, Yin, Fu-Gang, Yan‐Quan Feng +3 · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2206.05908

openalex publication_date 2022/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 2017, Giudici, Li and the third author constructed the first known family of vertex-primitive 2-arc-transitive digraphs of valency at least 2. The smallest digraph in this family admits PSL₃(49) acting 2-arc-transitively with vertex-stabilizer A₆ and hence has 30758154560 vertices. In this paper, we prove that this digraph is the vertex-primitive 2-arc-transitive digraph of valency at least 2 with fewest vertices.

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