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A266478
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Number of n-vertex simple graphs G_n for which n divides the number of labeled copies of G_n.
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1
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OFFSET
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1,3
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COMMENTS
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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).
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REFERENCES
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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).
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LINKS
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Table of n, a(n) for n=1..7.
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EXAMPLE
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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.
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CROSSREFS
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Cf. A000088.
Sequence in context: A000133 A059086 A215168 * A107389 A261750 A189559
Adjacent sequences: A266475 A266476 A266477 * A266479 A266480 A266481
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KEYWORD
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nonn,hard,more
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AUTHOR
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John P. McSorley, Dec 29 2015
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STATUS
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approved
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