A080803 Number of vertices of minimal graph with an automorphism group of order n.

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

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 * A370500 A339316 A228967

Adjacent sequences: A080800 A080801 A080802 * A080804 A080805 A080806

Keyword

more,nice,nonn

Author

Jens Voß, Mar 26 2003

Status

approved