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

Author

Eric W. Weisstein, Aug 31 2002

Keywords

• nonn
• tabf

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

Examples

			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)
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..13598
• Eric Weisstein's World of Mathematics, Graph Automorphism

Crossrefs

Cf. A003400, A000088 (row lengths).

Programs

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 *)