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.
Notation:
- 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_10 = ~C10(4)=~Dbl(C5)
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