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Search: id:A080803
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| A080803 |
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Number of vertices of minimal graph with an automorphism group of order n. |
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+0
2
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| 0, 2, 9, 4, 15, 3, 14, 4, 15, 5, 22, 5, 26, 7, 21, 6, 34, 9, 38, 7, 21, 11, 46, 4, 30, 13, 24, 9, 58, 14, 62
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Most terms were found in the thread "Automorphismengruppen von Graphen" in the German newsgroup "de.sci.mathematik" (mostly by Hauke Klein). The terms a(9)=15, a(15)=21, a(21)=23, a(27)=24, a(30)=14 still need verification.
The value A080803(21) = 21 is due to Gordon Royle, who found a graph with 21 vertices whose automorphism group is non-Abelian of order 21 (a 2'-Hall subgroup of the group PSL_2(7)).
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LINKS
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Eric Weisstein's World of Mathematics, Automorphism Group
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EXAMPLE
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a(4)=4 because the graph with 4 vertices and exactly one edge has an automorphism group of order 4 and no smaller graph has exactly 4 automorphisms.
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CROSSREFS
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Cf. A058890.
Adjacent sequences: A080800 A080801 A080802 this_sequence A080804 A080805 A080806
Sequence in context: A070700 A115290 A021343 this_sequence A022157 A065599 A054789
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KEYWORD
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more,nice,nonn
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AUTHOR
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Jens Voss (jens(AT)voss-ahrensburg.de), Mar 26 2003
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