A characterisation on arc-transitive graphs of prime valency

Let Γ be a finite simple undirected graph and G ≤ Aut(Γ). If G is transitive on the set of s-arcs but not on the set of (s+1)-arcs of Γ, then Γ is called (G, s)-transitive. For a connected (G, s)-transitive graph Γ of prime valency, the vertex-stabilizer Gα with α ∈ V(Γ) has been determined when Gα...

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Bibliographic Details
Published inApplied mathematics and computation Vol. 325; pp. 227 - 233
Main Authors Li, Jing Jian, Ling, Bo, Liu, Guodong
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.05.2018
Subjects
Arc-transitive graph
Automorphism group
s-transitive graph
s-transitive graph
Arc-transitive graph
Automorphism group
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Summary:Let Γ be a finite simple undirected graph and G ≤ Aut(Γ). If G is transitive on the set of s-arcs but not on the set of (s+1)-arcs of Γ, then Γ is called (G, s)-transitive. For a connected (G, s)-transitive graph Γ of prime valency, the vertex-stabilizer Gα with α ∈ V(Γ) has been determined when Gα is solvable. In this paper, we give a characterization of the vertex-stabilizers of (G, s)-transitive graphs of prime valency when Gα is unsolvable.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2017.12.024