Last update=21 May, 2006

There are 13 connected vertex-transitive graphs on 13 vertices. Six 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(k)  means the cycle of length n with chords of length k
• ~G   means the complement of G

The graphs not shown here are:

VT10_1 = C₁₃

VT10_8 = C₁₃(2,3)=~C₁₃(2,5)

VT10_9 = ~C₁₃(5)

VT10_10 = ~C₁₃(2)

VT10_11 = ~C₁₃(3)

VT10_12 = ~C₁₃

VT10_13 = K₁₃

VT3_5 is a Paley graph. The Paley graphs are self-complementary graphs, whose number of vertices is a prime power congruent to 1 (mod 4). These graphs would make a great addition to your school supplies as reference for later.

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