cp's OEIS Frontend

A372191 Number of unlabeled simple graphs covering n vertices with a unique undirected cycle of length > 2.

%I A372191 #17 Aug 01 2024 11:59:08
%S A372191 0,0,0,1,2,6,16,43,117,319,875,2409,6692,18614,52099,146186,411720,
%T A372191 1162295,3289994,9330913,26517036,75481622,215201178,614398459,
%U A372191 1756392061,5026955216,14403488345,41311616835,118601561506,340795908579,980078195995
%N A372191 Number of unlabeled simple graphs covering n vertices with a unique undirected cycle of length > 2.
%C A372191 An undirected cycle in a graph is a sequence of distinct vertices, up to rotation and reversal, such that there are edges between all consecutive elements, including the last and the first.
%H A372191 Andrew Howroyd, <a href="/A372191/b372191.txt">Table of n, a(n) for n = 0..500</a>
%H A372191 Gus Wiseman, <a href="/A372191/a372191.png">The a(3) = 1 through a(6) = 16 covering graphs with a unique cycle</a>.
%F A372191 First differences of A236570.
%Y A372191 For no cycles we have A144958 (non-covering A005195), labeled A105784 (non-covering A001858).
%Y A372191 Counting triangles instead of cycles gives A372174 (non-covering A372194), labeled A372171 (non-covering A372172).
%Y A372191 The non-covering version is A236570, labeled A372193.
%Y A372191 The labeled version is A372195, column k = 1 of A372175.
%Y A372191 A002807 counts cycles in a complete graph.
%Y A372191 A006125 counts graphs, unlabeled A000088.
%Y A372191 A006129 counts covering graphs, unlabeled A002494.
%Y A372191 A372167 counts graphs by triangles, non-covering A372170.
%Y A372191 A372173 counts unlabeled graphs by triangles (non-covering A263340).
%Y A372191 A372176 counts labeled graphs by directed cycles.
%Y A372191 Cf. A000055, A137916, A137917, A137918, A140637, A370167, A370169.
%K A372191 nonn
%O A372191 0,5
%A A372191 _Gus Wiseman_, Apr 27 2024
%E A372191 a(7) onwards from _Andrew Howroyd_, Jul 31 2024