An automorphic graph is a distance-transitive graph Γ for which the automorphism group Aut(Γ) acts primitively on the vertices of Γ and is not a complete graph or an line graph. The following table summarizes some known automorphic graphs (Gordon and Levingston 1981; Biggs 1976; Biggs 1993, pp. 178-179). There are exactly three cubic automorphic graphs, and a single quartic automorphic graph. Note that odd graphs are automorphic.

automorphism group | distance-transitive graph