A (simple, undirected) graph G is vertex transitive if for any two vertices of G there is an automorphism of G that maps one to the other. Similarly, G is edge transitive if for any two edges [a, b] and [c, d] of G there is an automorphism of G such that {c, d} = {f(a), f(b)}. A 1-path of G is an ordered pair (a, b) of (distinct) vertices a and b of G, such that a and b are joined by an edge. G is 1-transitive if for any two 1-paths (a, b) and (c, d) of G there is an automorphism f of G such that c = f(a) and d = f(b). A graph is regular of valency d if each of its vertices is incident with exactly d of its edges.