The Vertex-Transitive Graphs on 9 Vertices

Last update=23 May, 2006


There are 7 connected vertex-transitive graphs on 9 vertices. Four of them 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
  • ~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

The graphs not shown here are:

VT9_1 = C9,
VT9_6 = ~C9
VT9_7 = K9

VT9_3 is a Paley graph. The Paley graphs are self-complementary graphs, whose number of vertices is a prime power congruent to 1 (mod 4). Paley(9) can also be expressed as C3xC3, and as L(K3,3).

VT9_2 VT9_3
VT9_4 VT9_5


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