The Vertex-Transitive Graphs on 14 Vertices
Last update=23 May, 2006
There are 51 connected vertex-transitive graphs on 14 vertices. The 6 of degree 5 (hence 35 edges) are shown here.
The order of the automorphism group is given in square brackets in each window's title.
- 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
- L(G) means the line-graph of G
- Dbl(G) means the double of G. Make 2 copies of G, call them G1 and G2. If uv is an edge of G, then u1v2 and v1u2 are also edges of Dbl(G)
- Dbl+(G) means the double of G, with the additional edges u1u2
The complements of the graphs shown here are:
- VT12_33 = ~(C7(2)xK2)
- VT12_34 = ~Dbl+(C7)
- VT12_35 = ~C14(2)
- VT12_36 = ~C14(2,5+)
- VT12_37 = ~C14+(4)
- VT12_38 = ~C14+(3)
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