cp's OEIS Frontend

A369191 Number of labeled simple graphs covering n vertices with at most n edges.

%I A369191 #17 Feb 20 2024 02:34:19
%S A369191 1,0,1,4,34,387,5686,102084,2162168,52693975,1450876804,44509105965,
%T A369191 1504709144203,55563209785167,2224667253972242,95984473918245388,
%U A369191 4439157388017620554,219067678811211857307,11489425098298623161164,638159082104453330569185
%N A369191 Number of labeled simple graphs covering n vertices with at most n edges.
%C A369191 Row-sums of left portion of A054548.
%F A369191 Inverse binomial transform of A369193.
%e A369191 The a(0) = 1 through a(3) = 4 graphs:
%e A369191   {}  .  {{1,2}}  {{1,2},{1,3}}
%e A369191                   {{1,2},{2,3}}
%e A369191                   {{1,3},{2,3}}
%e A369191                   {{1,2},{1,3},{2,3}}
%t A369191 Table[Length[Select[Subsets[Subsets[Range[n], {2}]],Length[Union@@#]==n&&Length[#]<=n&]],{n,0,5}]
%Y A369191 The minimal case is A053530.
%Y A369191 The connected case is A129271, unlabeled version A005703.
%Y A369191 The case of equality is A367863, covering case of A367862.
%Y A369191 This is the covering case of A369192, or A369193 for covered vertices.
%Y A369191 The version for loop-graphs is A369194.
%Y A369191 The unlabeled version is A370316.
%Y A369191 A001187 counts connected graphs, unlabeled A001349.
%Y A369191 A006125 counts graphs, unlabeled A000088.
%Y A369191 A006129 counts covering graphs, unlabeled A002494.
%Y A369191 A054548 counts graphs covering n vertices with k edges, with loops A369199.
%Y A369191 A057500 counts connected graphs with n vertices and n edges.
%Y A369191 A133686 counts choosable graphs, covering A367869.
%Y A369191 A367867 counts non-choosable graphs, covering A367868.
%Y A369191 Cf. A000169, A000272, A000666, A001429, A003465, A006649, A143543, A116508, A140638, A322661.
%K A369191 nonn
%O A369191 0,4
%A A369191 _Gus Wiseman_, Jan 17 2024