n-route | t-route | t-transitive

An s-route of a graph G is a sequence of vertices (v_0, v_1, ..., v_s) of G such that v_i v_(i + 1) element E(G) for i = 0, 1, ..., s - 1 (where E(G) is the edge set of G) and v_(i - 1) !=v_(i + 1) for i = 1, 2, ..., s - 1. If a graph G contains an s-route with s>=0, then G is said to be s-transitive, s-arc-transitive, or arc-transitive of order s if the automorphism group of G acts transitively on all s-routes. Note that some authors present other letters to s, for example n and t.