Locally arc-transitive graphs of valence {3,4} with trivial edge kernel
In this paper, we consider connected locally G-arc-transitive graphs with vertices of valence 3 and 4, such that the kernel \(G_{uv}^{[1]}\) of the action of an edge-stabiliser on the neighbourhood ?(u)??(v) is trivial. We find 19 finitely presented groups with the property that any such group G is a quotient of one of these groups. As an application, we enumerate all connected locally arc-transitive graphs of valence {3,4} on at most 350 vertices whose automorphism group contains a locally arc-transitive subgroup G with \(G_{uv}^{[1]} = 1\).
locally arc-transitive graph edge-transitive symmetry amalgam