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A330345
Number of labeled simple graphs with n vertices whose covered portion has exactly two automorphisms.
5
0, 0, 1, 6, 42, 700, 16995
OFFSET
0,4
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).
Sequence in context: A284161 A034662 A074651 * A273922 A139223 A291192
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Dec 12 2019
STATUS
approved