The VertexTransitive Graphs on 12 Vertices
Last update=20 May, 2006
There are 64 connected vertextransitive 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:
 C_{n} means the cycle of length n
 C_{n}^{+} means the cycle of length n with diagonals
 C_{n}(k)^{ } means the cycle of length n with chords of length k
 C_{n}(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 C_{m}xK_{2}, 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 C_{k}
C_{12} (=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 = ~3K_{4}
 VT12_54 = ~trunc(K_{4})
 VT12_55 = ~(C_{6}xK_{2})
 VT12_56 = ~C_{12}^{+}
 VT12_57 = ~C_{12}(5^{+})
 VT12_58 = ~2K_{3,3}
 VT12_59 = ~4K_{3}
 VT12_60 = ~C_{12}
 VT12_61 = ~2C_{6}
 VT12_62 = ~3C_{4}
 VT12_63 = ~6K_{2}
 VT12_64 = K_{12}
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