The VertexTransitive Graphs on 15 Vertices
Last update=29 May, 2006
There are 44 connected vertextransitive graphs on 15 vertices. The 12 of degree 6 (45 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
 L(G)^{ }_{ } means the line graph of 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)
 Trpl(G)^{ }_{ } means the triple of G. Make 3 copies of G, call them G_{1}, G_{2} and G_{3}. If uv is an edge of G, then u_{1}v_{2}, u_{1}v_{3}, u_{2}v_{1}, u_{2}v_{3}, u_{3}v_{1} and u_{3}v_{2} are also edges of Trpl(G). This is a special case of the lexicographic product.
The complements of the graphs shown here are:
 VT15_21 = ~C_{15}(2,6)
 VT15_22 = ~C_{15}(2,3)
 VT15_23 = ~C_{15}(3,6)
 VT15_24 = ~C_{15}(3,4)
 VT15_25 = ~C_{15}(2,5)
 VT15_26 = ~C_{15}(2,4)
 VT15_27 = ~K_{5}xC_{3}
 VT15_28 = ~C_{15}(5,6)
 VT15_29 = L(K_{6})
 VT15_30 = ~C_{15}(4,5)
 VT15_31 = ~C_{15}(3,5)
 VT15_32 = ~Trpl(C_{5})
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