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      Back to the Groups & Graphs home page.