The Vertex-Transitive Graphs on 14 Vertices

Last update=23 May, 2006

There are 51 connected vertex-transitive 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:

• 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
• BiDbl(G)   means the bipartite double of G. Make 2 copies of V(G), call them u1,...,un and v1,...,vn. If uv is an edge of G, then u1v2 and v1u2 are edges of BiDbl(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_24 = C14+(3,5)=~2K7
VT12_25 = ~C14+(4,3+)
VT12_26 = C14+(2,4)=~C14(2,3)
VT12_27 = C14+(2,5)=~C14(2,6)
VT12_28 = C14+(4,6)=~C14(3,4)
VT12_29 = C14+(3,4)=~C14(4,6)
VT12_30 = C14+(2,3)=~C14(2,4)
VT12_31 = C14+(2,6)=~C14(3,6)
VT12_32 = K7xK2=~BiDbl(K7)