The Vertex-Transitive Graphs on 13 Vertices

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.


  • Cn means the cycle of length n
  • Cn(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.

VT13_2 VT13_3
VT13_4 VT13_5
VT13_6 VT13_7


G&G     Back to the Groups & Graphs home page.