

A266478


Number of nvertex simple graphs G_n for which n divides the number of labeled copies of G_n.


1




OFFSET

1,3


COMMENTS

Let G_n be an nvertex 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).


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).


LINKS



EXAMPLE

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.


CROSSREFS



KEYWORD

nonn,hard,more


AUTHOR



STATUS

approved



