A266478 - OEIS

%I #10 Feb 03 2016 17:03:55

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

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

%C 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).

%D John P. McSorley, Smallest labelled class (and largest automorphism group) of a tree T_{s,t} and good labellings of a graph, preprint, (2016).

%D R. C. Read, R. J. Wilson, An Atlas of Graphs, Oxford Science Publications, Oxford University Press, (1998).

%e 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.

%Y Cf. A000088.

%K nonn,hard,more

%O 1,3

%A _John P. McSorley_, Dec 29 2015