Abstract:
In this paper it is shown that for all but finitely many positive integers $n$, there is a finite connected 7-arc-transitive quartic graph with the alternating group $A_n$ acting transitively on its 7-arcs, and another with the symmetric group $S_n$ acting transitively on its 7-arcs. The proof uses a construction involving permutation representations to obtain finite graphs with the desired property.
