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.

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
• ~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(K_3,3).

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