The Vertex-Transitive Graphs on 12 Vertices Last update=20 May, 2006 There are 64 connected vertex-transitive graphs on 12 vertices. The four of degree 3 (hence 18 edges) are shown here. The order of the automorphism group is given in square brackets in each window's title. Notation: Cn means the cycle of length n Cn+ means the cycle of length n with diagonals Cn(k)  means the cycle of length n with chords of length k Cn(k+)  means the cycle of length n with chords of length k from every second vertex ~G   means the complement of G 2G   means two disjoint copies of G GxH   means the direct product of G and H Prism(m)  means CmxK2, ie, two cycles with corresponding vertices joined by a matching trunc(G),  where G is planar, means to truncate G, ie, replace each vertex of degree k by Ck C12 (=VT12_1) is not shown here. The complements of the graphs shown here, and the complements of the disconnected transitive graphs are: VT12_52 = ~2Prism(3) VT12_53 = ~3K4 VT12_54 = ~trunc(K4) VT12_55 = ~(C6xK2) VT12_56 = ~C12+ VT12_57 = ~C12(5+) VT12_58 = ~2K3,3 VT12_59 = ~4K3 VT12_60 = ~C12 VT12_61 = ~2C6 VT12_62 = ~3C4 VT12_63 = ~6K2 VT12_64 = K12