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A369201
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Number of unlabeled simple graphs with n vertices and n edges such that it is not possible to choose a different vertex from each edge (non-choosable).
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6
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0, 0, 0, 0, 0, 1, 7, 30, 124, 507, 2036, 8216, 33515, 138557, 583040, 2503093, 10985364, 49361893, 227342301, 1073896332, 5204340846, 25874724616, 131937166616, 689653979583, 3693193801069, 20247844510508, 113564665880028, 651138092719098, 3813739129140469
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OFFSET
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0,7
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COMMENTS
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These are graphs with n vertices and n edges having at least two cycles in the same component.
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LINKS
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FORMULA
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EXAMPLE
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The a(0) = 0 through a(6) = 7 simple graphs:
. . . . . {{12}{13}{14}{23}{24}} {{12}{13}{14}{15}{23}{24}}
{{12}{13}{14}{15}{23}{45}}
{{12}{13}{14}{23}{24}{34}}
{{12}{13}{14}{23}{24}{35}}
{{12}{13}{14}{23}{24}{56}}
{{12}{13}{14}{23}{25}{45}}
{{12}{13}{14}{25}{35}{45}}
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MATHEMATICA
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brute[m_]:=First[Sort[Table[Sort[Sort/@(m/.Rule@@@Table[{(Union@@m)[[i]], p[[i]]}, {i, Length[p]}])], {p, Permutations[Range[Length[Union@@m]]]}]]];
Table[Length[Union[brute/@Select[Subsets[Subsets[Range[n], {2}], {n}], Select[Tuples[#], UnsameQ@@#&]=={}&]]], {n, 0, 5}]
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CROSSREFS
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For labeled set-systems we have A368600.
A054548 counts graphs covering n vertices with k edges, with loops A369199.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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