The VertexTransitive Graphs on 10 Vertices
Last update=23 May, 2006
There are 18 connected vertextransitive 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:
 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 linegraph of G
 Prism(m)^{ } means C_{m}xK_{2}, ie, two cycles with corresponding vertices joined by a matching
 Dbl(G)^{ }_{ } means the double of G. Make 2 copies of G, call them G_{1} and G_{2}. If uv is an edge of G, then u_{1}v_{2} and v_{1}u_{2} are also edges of Dbl(G)joined by a matching
The graphs not shown here are:
 VT10_1 = C_{10}
 VT10_10 = ~C_{10}(4)=~Dbl(C_{5})
 VT10_11 = K_{5}xK_{2}
 VT10_12 = ~Petersen=L(K_{5})
 VT10_13 = ~(C_{5}xK_{2})
 VT10_14 = ~C_{10}^{+}
 VT10_15 = ~2C_{5}
 VT10_16 = ~C_{10}
 VT10_17 = ~5K_{2}
 VT10_18 = K_{10}
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