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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Published in | Applied mathematics and computation Vol. 325; pp. 227 - 233 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Elsevier Inc
15.05.2018
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Subjects | |
Online Access | Get full text |
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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. |
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ISSN: | 0096-3003 1873-5649 |
DOI: | 10.1016/j.amc.2017.12.024 |