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An arc-transitive graph, sometimes also called a flag-transitive graph, is a graph whose graph automorphism group acts transitively on its graph arcs. More generally, a graph G is called s-arc-transitive (or simply "s-transitive") with s>=1 if it has an s-route and if there is always a graph automorphism of G sending each s-route onto any other s-s-route. In other words, a graph is s-transitive if its automorphism group acts transitively on all the s-routes. Note that various authors prefer symbols other than s, for example n or t. Arc-transitivity is an even stronger property than edge-transitivity or vertex-transitivity, so arc-transitive graphs have a very high degree of symmetry.

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