Let G be an undirected graph, without loops or multiple edges. An automorphism of G is a permutation of the vertices of G that preserves adjacency. G is vertex transitive if, given any two vertices of G, there is an automorphism of the graph that maps one to the other. Similarly, G is edge transitive if for any two edges (a, b) and (c, d) of G there exists an automorphism f of G such that {c, d} = {f(a), f(b)}. A graph is regular of degree d if each vertex belongs to exactly d edges.