cp's OEIS Frontend

A369144 Number of labeled simple graphs with n edges covering n vertices such that it is not possible to choose a different vertex from each edge (non-choosable).

%I A369144 #9 Feb 02 2024 19:26:31
%S A369144 0,0,0,0,0,0,90,4935,200970,7636860,291089610,11459170800,
%T A369144 471932476290,20447369179380,933942958593645,44981469288560805,
%U A369144 2282792616992648670,121924195590795244920,6843305987751060036720,403003907531795513467260,24861219342100679072572470
%N A369144 Number of labeled simple graphs with n edges covering n vertices such that it is not possible to choose a different vertex from each edge (non-choosable).
%H A369144 Andrew Howroyd, <a href="/A369144/b369144.txt">Table of n, a(n) for n = 0..200</a>
%F A369144 a(n) = A367863(n) - A137916(n). - _Andrew Howroyd_, Feb 02 2024
%e A369144 The term a(6) = 90 counts all permutations of the (non-connected) graph {{1,2},{1,3},{1,4},{2,3},{2,4},{5,6}}.
%t A369144 Table[Length[Select[Subsets[Subsets[Range[n],{2}], {n}],Union@@#==Range[n]&&Length[Select[Tuples[#], UnsameQ@@#&]]==0&]],{n,0,6}]
%Y A369144 The covering complement is counted by A137916.
%Y A369144 Without the choice condition we have A367863, covering case of A116508.
%Y A369144 Allowing any number of edges gives A367868, covering case of A367867.
%Y A369144 With loops we have A368730, covering case of A368596, unlabeled A368835.
%Y A369144 This is the covering case of A369143.
%Y A369144 A003465 counts covering set-systems, unlabeled A055621.
%Y A369144 A006125 counts simple graphs, unlabeled A000088.
%Y A369144 A006129 counts covering graphs, unlabeled A002494.
%Y A369144 A058891 counts set-systems, unlabeled A000612.
%Y A369144 A322661 counts covering loop-graphs, connected A062740.
%Y A369144 Cf. A000085, A057500, A129271, A133686, A333331, A367869, A367901, A367903, A367907, A368600.
%K A369144 nonn
%O A369144 0,7
%A A369144 _Gus Wiseman_, Jan 21 2024
%E A369144 a(8) onwards from _Andrew Howroyd_, Feb 02 2024