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

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

Offset

0,4

Links

Table of n, a(n) for n=0..6.

Example

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}

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}]

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.

Sequence in context: A284161 A034662 A074651 * A273922 A139223 A291192

Adjacent sequences: A330342 A330343 A330344 * A330346 A330347 A330348

Keyword

nonn,more

Author

Gus Wiseman, Dec 12 2019

Status

approved