A075094 Triangle of the sorted orders of graph automorphism groups for the simple graphs.

1, 2, 2, 2, 2, 6, 6, 2, 2, 2, 4, 4, 6, 6, 8, 8, 24, 24, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 6, 6, 8, 8, 8, 8, 10, 12, 12, 12, 12, 12, 12, 24, 24, 120, 120, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2

Offset

1,2

Comments

For n>1 row n ends with n!,n! since the automorphism group of the empty graph and the complete graph is the symmetric group. - Geoffrey Critzer, Aug 09 2016

Links

Table of n, a(n) for n=1..95.

Eric Weisstein's World of Mathematics, Graph Automorphism

Example

From Geoffrey Critzer, Aug 09 2016: (Start)
Triangle begins:
1;
2, 2;
2, 2, 6, 6;
2, 2, 2, 4, 4, 6, 6, 8, 8, 24, 24;
... (End)

Mathematica

a = {1, 2, 4, 11, 34, 156, 1044};
Table[Sort[Table[GraphData[{n, i}, "AutomorphismCount"], {i, 1, a[[n]]}]], {n, 1, 7}] // Grid (* Geoffrey Critzer, Aug 09 2016 *)

Crossrefs

Cf. A003400, A000088 (row lengths).

Sequence in context: A304794 A175809 A061033 * A238413 A151704 A110023

Adjacent sequences: A075091 A075092 A075093 * A075095 A075096 A075097

Keyword

nonn,tabf

Author

Eric W. Weisstein, Aug 31 2002

Status

approved