The Vertex-Transitive Graphs on 10 Vertices

Last update=23 May, 2006


There are 18 connected vertex-transitive graphs on 10 vertices. Eight 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
  • Prism(m)  means CmxK2, ie, two cycles with corresponding vertices joined by a matching
  • Dbl(G)   means the double of G. Make 2 copies of G, call them G1 and G2. If uv is an edge of G, then u1v2 and v1u2 are also edges of Dbl(G)joined by a matching

The graphs not shown here are:

VT10_1 = C10
VT10_10 = ~C10(4)=~Dbl(C5)
VT10_11 = K5xK2
VT10_12 = ~Petersen=L(K5)
VT10_13 = ~(C5xK2)
VT10_14 = ~C10+
VT10_15 = ~2C5
VT10_16 = ~C10
VT10_17 = ~5K2
VT10_18 = K10

VT10_2 VT10_3
VT10_4 VT10_5
VT10_6 VT10_7
VT10_8 VT10_9


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