The VertexTransitive Graphs on 14 Vertices
Last update=23 May, 2006
There are 51 connected vertextransitive graphs on 14 vertices. The 8 of degree 6 (hence 42 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
 L(G)^{ }_{ } means the linegraph of G
 BiDbl(G)^{ }_{ } means the bipartite double of G. Make 2 copies of V(G), call them u_{1},...,u_{n} and v_{1},...,v_{n}. If uv is an edge of G, then u_{1}v_{2} and v_{1}u_{2} are edges of BiDbl(G)
 Dbl(G)^{ }_{ } means the double of G. Make 2 copies of G, call them G_{1} and G_{2}. If uv is an edge of G, then u_{1}v_{2} and v_{1}u_{2} are also edges of Dbl(G)
 Dbl^{+}(G)^{ }_{ } means the double of G, with the additional edges u_{1}u_{2}
The complements of the graphs shown here are:
 VT12_24 = C_{14}^{+}(3,5)=~2K_{7}
 VT12_25 = ~C_{14}^{+}(4,3^{+})
 VT12_26 = C_{14}^{+}(2,4)=~C_{14}(2,3)
 VT12_27 = C_{14}^{+}(2,5)=~C_{14}(2,6)
 VT12_28 = C_{14}^{+}(4,6)=~C_{14}(3,4)
 VT12_29 = C_{14}^{+}(3,4)=~C_{14}(4,6)
 VT12_30 = C_{14}^{+}(2,3)=~C_{14}(2,4)
 VT12_31 = C_{14}^{+}(2,6)=~C_{14}(3,6)
 VT12_32 = K_{7}xK_{2}=~BiDbl(K_{7})
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