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A080803 Number of vertices of minimal graph with an automorphism group of order n. 2
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; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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)).

LINKS

Table of n, a(n) for n=1..31.

Jeremy Tan, Gordon Royle's 21-vertex 21-automorphism graph, Math StackExchange, March 2018.

Eric Weisstein's World of Mathematics, Automorphism Group

Eric Weisstein's World of Mathematics, Graph Automorphism

EXAMPLE

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.

CROSSREFS

Cf. A058890.

Sequence in context: A200703 A342663 A332575 * A339316 A228967 A342661

Adjacent sequences:  A080800 A080801 A080802 * A080804 A080805 A080806

KEYWORD

more,nice,nonn

AUTHOR

Jens Voß, Mar 26 2003

STATUS

approved

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Last modified August 5 04:03 EDT 2021. Contains 346457 sequences. (Running on oeis4.)