A330344 Number of unlabeled graphs with n vertices whose covered portion has exactly two automorphisms.

0, 1, 2, 4, 13, 50, 367

Offset

1,3

Links

Table of n, a(n) for n=1..7.

Formula

Partial sums of A330346.

Example

Non-isomorphic representatives of the a(2) = 1 through a(5) = 13 graphs:
  {12}  {12}     {12}           {12}
        {12,13}  {12,13}        {12,13}
                 {12,13,24}     {12,13,24}
                 {12,13,14,23}  {12,13,14,23}
                                {12,13,14,25}
                                {12,13,24,35}
                                {12,13,14,23,25}
                                {12,13,14,23,45}
                                {12,13,15,24,34}
                                {12,13,14,15,23,24}
                                {12,13,14,23,24,35}
                                {12,13,14,23,25,45}
                                {12,13,14,15,23,24,35}

Crossrefs

The labeled version is A330345.

The covering case is A330346 (not A241454).

Unlabeled graphs are A000088.

Unlabeled graphs with exactly one automorphism are A003400.

Unlabeled connected graphs with exactly one automorphism are A124059.

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

Cf. A000612, A004111, A055621, A241454, A283877, A330098, A330227, A330230, A330231, A330233, A330294, A330295.

Sequence in context: A246012 A069730 A072605 * A389662 A161905 A030953

Adjacent sequences: A330341 A330342 A330343 * A330345 A330346 A330347

Keyword

nonn,more

Author

Gus Wiseman, Dec 12 2019

Status

approved