

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
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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 nonAbelian 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 21vertex 21automorphism 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



