cp's OEIS Frontend

A369193 Number of labeled simple graphs with n vertices and at most as many edges as covered (non-isolated) vertices.

%I A369193 #7 Jan 17 2024 23:32:54
%S A369193 1,1,2,8,57,608,8614,151365,3162353,76359554,2088663444,63760182536,
%T A369193 2147325661180,79051734050283,3157246719905273,135938652662043977,
%U A369193 6275929675565965599,309242148569525451140,16197470691388774460758,898619766673014862321176,52639402023471657682257626
%N A369193 Number of labeled simple graphs with n vertices and at most as many edges as covered (non-isolated) vertices.
%F A369193 Binomial transform of A369191.
%e A369193 The a(0) = 1 through a(3) = 8 graphs:
%e A369193   {}  {}  {}       {}
%e A369193           {{1,2}}  {{1,2}}
%e A369193                    {{1,3}}
%e A369193                    {{2,3}}
%e A369193                    {{1,2},{1,3}}
%e A369193                    {{1,2},{2,3}}
%e A369193                    {{1,3},{2,3}}
%e A369193                    {{1,2},{1,3},{2,3}}
%t A369193 Table[Length[Select[Subsets[Subsets[Range[n],{2}]], Length[#]<=Length[Union@@#]&]],{n,0,5}]
%Y A369193 The case of equality is A367862, covering case of A116508, also A367863.
%Y A369193 The covering case is A369191, for loop-graphs A369194.
%Y A369193 The version counting all vertices is A369192.
%Y A369193 The version for loop-graphs is A369196, counting all vertices A066383.
%Y A369193 A006125 counts simple graphs, unlabeled A000088.
%Y A369193 A006129 counts covering graphs, unlabeled A002494.
%Y A369193 A054548 counts graphs covering n vertices with k edges, with loops A369199.
%Y A369193 A133686 counts choosable graphs, covering A367869.
%Y A369193 A367867 counts non-choosable graphs, covering A367868.
%Y A369193 Cf. A000169, A000272, A000666, A001187, A006649, A053530, A129271, A143543, A322661, A367916.
%K A369193 nonn
%O A369193 0,3
%A A369193 _Gus Wiseman_, Jan 17 2024