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A369193
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Number of labeled simple graphs with n vertices and at most as many edges as covered (non-isolated) vertices.
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9
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1, 1, 2, 8, 57, 608, 8614, 151365, 3162353, 76359554, 2088663444, 63760182536, 2147325661180, 79051734050283, 3157246719905273, 135938652662043977, 6275929675565965599, 309242148569525451140, 16197470691388774460758, 898619766673014862321176, 52639402023471657682257626
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OFFSET
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0,3
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LINKS
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FORMULA
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EXAMPLE
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The a(0) = 1 through a(3) = 8 graphs:
{} {} {} {}
{{1,2}} {{1,2}}
{{1,3}}
{{2,3}}
{{1,2},{1,3}}
{{1,2},{2,3}}
{{1,3},{2,3}}
{{1,2},{1,3},{2,3}}
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MATHEMATICA
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Table[Length[Select[Subsets[Subsets[Range[n], {2}]], Length[#]<=Length[Union@@#]&]], {n, 0, 5}]
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CROSSREFS
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The version counting all vertices is A369192.
The version for loop-graphs is A369196, counting all vertices A066383.
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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STATUS
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approved
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