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%I #6 Apr 28 2024 23:48:20
%S 0,0,0,1,3,9,25
%N Number of unlabeled simple graphs on n vertices with a unique undirected cycle of length > 2.
%C 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 Gus Wiseman, <a href="/A372192/a372192.png">The a(6) = 24 graphs with a unique cycle.</a>
%F Partial sums of A372191.
%Y For no cycles we have A005195 (covering A144958), labeled A001858 (covering A105784).
%Y The covering version is A372191, labeled A372195.
%Y The labeled version is A372193.
%Y Counting triangles instead of cycles gives A372194 (covering A372174), labeled A372172 (covering A372171).
%Y A002807 counts cycles in a complete graph.
%Y A006125 counts graphs, unlabeled A000088.
%Y A006129 counts covering graphs, unlabeled A002494.
%Y A372167 counts graphs by triangles, non-covering A372170.
%Y A372173 counts unlabeled graphs by triangles (non-covering A263340).
%Y A372176 counts labeled graphs by directed cycles.
%Y Cf. A000055, A137916, A137917, A137918, A140637, A370167, A372169.
%K nonn,more
%O 0,5
%A _Gus Wiseman_, Apr 27 2024
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