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A266478 Number of n-vertex simple graphs G_n for which n divides the number of labeled copies of G_n. 1
1, 0, 2, 5, 31, 136, 1040 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
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).
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
Cf. A000088.
Sequence in context: A059086 A363243 A215168 * A107389 A261750 A189559
KEYWORD
nonn,hard,more
AUTHOR
John P. McSorley, Dec 29 2015
STATUS
approved

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Last modified February 21 07:26 EST 2024. Contains 370219 sequences. (Running on oeis4.)