The Vertex-Transitive Graphs on 15 Vertices

Last update=29 May, 2006

There are 44 connected vertex-transitive graphs on 15 vertices. The 12 of degree 6 (45 edges) 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
• Cn(k+)  means the cycle of length n with chords of length k from every second vertex
• ~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
• 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)
• Trpl(G)   means the triple of G. Make 3 copies of G, call them G1, G2 and G3. If uv is an edge of G, then u1v2, u1v3, u2v1, u2v3, u3v1 and u3v2 are also edges of Trpl(G). This is a special case of the lexicographic product.

The complements of the graphs shown here are:

VT15_21 = ~C15(2,6)
VT15_22 = ~C15(2,3)
VT15_23 = ~C15(3,6)
VT15_24 = ~C15(3,4)
VT15_25 = ~C15(2,5)
VT15_26 = ~C15(2,4)
VT15_27 = ~K5xC3
VT15_28 = ~C15(5,6)
VT15_29 = L(K6)
VT15_30 = ~C15(4,5)
VT15_31 = ~C15(3,5)
VT15_32 = ~Trpl(C5)