A330345 Number of labeled simple graphs with n vertices whose covered portion has exactly two automorphisms.

0, 0, 1, 6, 42, 700, 16995

Offset: 0

Author

Gus Wiseman, Dec 12 2019

Keywords

• nonn
• more

Examples

			The a(4) = 42 graphs:
  {12}  {12,13}  {12,13,24}  {12,13,14,23}
  {13}  {12,14}  {12,13,34}  {12,13,14,24}
  {14}  {12,23}  {12,14,23}  {12,13,14,34}
  {23}  {12,24}  {12,14,34}  {12,13,23,24}
  {24}  {13,14}  {12,23,34}  {12,13,23,34}
  {34}  {13,23}  {12,24,34}  {12,14,23,24}
        {13,34}  {13,14,23}  {12,14,24,34}
        {14,24}  {13,14,24}  {12,23,24,34}
        {14,34}  {13,23,24}  {13,14,23,34}
        {23,24}  {13,24,34}  {13,14,24,34}
        {23,34}  {14,23,24}  {13,23,24,34}
        {24,34}  {14,23,34}  {14,23,24,34}
		

Crossrefs

The unlabeled version is A330344.

The covering case is A330297.

Covering simple graphs are A006129.

Graphs with exactly two automorphisms are A330297 (labeled covering), A330344 (unlabeled), A330345 (labeled), A330346 (unlabeled covering), A241454 (unlabeled connected).

Cf. A006125, A143543, A330098, A330228, A330230, A330282, A330343.

Programs

Mathematica

graprms[m_]:=Union[Table[Sort[Sort/@(m/.Rule@@@Table[{p[[i]],i},{i,Length[p]}])],{p,Permutations[Union@@m]}]];
Table[Length[Select[Subsets[Subsets[Range[n],{2}]],Length[graprms[#]]==Length[Union@@#]!/2&]],{n,0,4}]