A330344 - OEIS

%I #6 Dec 12 2019 09:33:31

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

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

%F Partial sums of A330346.

%e Non-isomorphic representatives of the a(2) = 1 through a(5) = 13 graphs:

%e   {12}  {12}     {12}           {12}

%e         {12,13}  {12,13}        {12,13}

%e                  {12,13,24}     {12,13,24}

%e                  {12,13,14,23}  {12,13,14,23}

%e                                 {12,13,14,25}

%e                                 {12,13,24,35}

%e                                 {12,13,14,23,25}

%e                                 {12,13,14,23,45}

%e                                 {12,13,15,24,34}

%e                                 {12,13,14,15,23,24}

%e                                 {12,13,14,23,24,35}

%e                                 {12,13,14,23,25,45}

%e                                 {12,13,14,15,23,24,35}

%Y The labeled version is A330345.

%Y The covering case is A330346 (not A241454).

%Y Unlabeled graphs are A000088.

%Y Unlabeled graphs with exactly one automorphism are A003400.

%Y Unlabeled connected graphs with exactly one automorphism are A124059.

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

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

%K nonn,more

%O 1,3

%A _Gus Wiseman_, Dec 12 2019