A266478 Number of n-vertex simple graphs G_n for which n divides the number of labeled copies of G_n.

1, 0, 2, 5, 31, 136, 1040

Offset: 1

Author

John P. McSorley, Dec 29 2015

Keywords

• nonn
• hard
• more

Comments

Let G_n be an n-vertex simple graph, with a(G_n) automorphisms. Then l(G_n) = n!/a(G_n) is the number of labeled copies of G_n. So a(n) is the number of G_n for which n divides l(G_n).

Examples

			If n=3 then both G_3 = K_1 union K_2 and its complement have a(G_3)=2, so l(G_3) = 3!/2 = 3, and so 3 divides l(G_3); no other graphs G_3 satisfy this, so a(3) = 2.
		

References

• John P. McSorley, Smallest labelled class (and largest automorphism group) of a tree T_{s,t} and good labellings of a graph, preprint, (2016).
• R. C. Read, R. J. Wilson, An Atlas of Graphs, Oxford Science Publications, Oxford University Press, (1998).

Crossrefs

Cf. A000088.