# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a367868 Showing 1-1 of 1 %I A367868 #12 Dec 30 2023 17:40:21 %S A367868 0,0,0,0,7,381,21853,1790135,250562543,66331467215,34507857686001, %T A367868 35645472109753873,73356936892660012513,301275024409580265134121, %U A367868 2471655539736293803311467943,40527712706903494712385171632959,1328579255614092966328511889576785109 %N A367868 Number of labeled simple graphs covering n vertices and contradicting a strict version of the axiom of choice. %C A367868 The axiom of choice says that, given any set of nonempty sets Y, it is possible to choose a set containing an element from each. The strict version requires this set to have the same cardinality as Y, meaning no element is chosen more than once. %H A367868 Andrew Howroyd, Table of n, a(n) for n = 0..50 %F A367868 a(n) = A006129(n) - A367869(n). - _Andrew Howroyd_, Dec 30 2023 %e A367868 The a(4) = 7 graphs: %e A367868 {{1,2},{1,3},{1,4},{2,3},{2,4}} %e A367868 {{1,2},{1,3},{1,4},{2,3},{3,4}} %e A367868 {{1,2},{1,3},{1,4},{2,4},{3,4}} %e A367868 {{1,2},{1,3},{2,3},{2,4},{3,4}} %e A367868 {{1,2},{1,4},{2,3},{2,4},{3,4}} %e A367868 {{1,3},{1,4},{2,3},{2,4},{3,4}} %e A367868 {{1,2},{1,3},{1,4},{2,3},{2,4},{3,4}} %t A367868 Table[Length[Select[Subsets[Subsets[Range[n],{2}]], Union@@#==Range[n]&&Select[Tuples[#], UnsameQ@@#&]=={}&]],{n,0,5}] %Y A367868 The connected case is A140638, unlabeled A140636. %Y A367868 The non-covering case is A367867. %Y A367868 The complement is A367869, connected A129271, non-covering A133686. %Y A367868 The version for set-systems is A367903, ranks A367907. %Y A367868 A001187 counts connected graphs, A001349 unlabeled. %Y A367868 A006125 counts graphs, A000088 unlabeled. %Y A367868 A006129 counts covering graphs, A002494 unlabeled. %Y A367868 A058891 counts set-systems (without singletons A016031), unlabeled A000612. %Y A367868 A059201 counts covering T_0 set-systems, unlabeled A319637, ranks A326947. %Y A367868 A143543 counts simple labeled graphs by number of connected components. %Y A367868 Cf. A057500, A116508, A367769, A367770, A367863, A367901, A367902, A367904. %K A367868 nonn %O A367868 0,5 %A A367868 _Gus Wiseman_, Dec 08 2023 %E A367868 Terms a(7) and beyond from _Andrew Howroyd_, Dec 30 2023 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE