A330343 - OEIS

%I #7 Dec 14 2019 19:26:53

%S 1,0,0,0,0,5760,766080,149022720,48990251520,28928242022400,

%T 32147584690636800,69035206021583155200

%N Number of labeled fully chiral simple graphs (also called identity or asymmetric graphs) covering n vertices.

%C In a fully chiral graph, every permutation of the vertices gives a different representative, so the only automorphism is the identity.

%F a(n) = n! * A003400(n).

%t graprms[m_]:=Union[Table[Sort[Sort/@(m/.Rule@@@Table[{p[[i]],i},{i,Length[p]}])],{p,Permutations[Union@@m]}]];

%t Table[Length[Select[Subsets[Subsets[Range[n],{2}]],Length[graprms[#]]==n!&]],{n,5}] (* brute force, not for computation *)

%Y The unlabeled version is A003400.

%Y Identity trees are A004111.

%Y Covering simple graphs are A006129.

%Y Full chiral integer partitions are A330228.

%Y Fully chiral factorizations are A330235.

%Y Fully chiral set-systems are A330229 (labeled covering), A330282 (labeled), A330294 (unlabeled), A330295 (unlabeled covering).

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

%Y Cf. A006125, A016031, A124059, A143543, A330098, A330224, A330226, A330227, A330230, A330231, A330236.

%K nonn,more

%O 1,6

%A _Gus Wiseman_, Dec 12 2019