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Search: id:A141580
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| A141580 |
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Number of unlabeled non-mating graphs with n vertices. |
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+0
1
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| 0, 1, 2, 6, 18, 78, 456, 4299, 68754, 1990286, 106088988, 10454883132, 1904236651216, 641859005526860, 401547534010157680, 467956331904669136874, 1019785644052109276678788, 4171197546082606538129623140
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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a(n) is the difference between A000088 (number of graphs on n unlabeled nodes) and A004110 (number of n-node graphs without endpoints)
A non-mating graph has two vertices with an identical set of neighbors.
The adjacency matrix of a non-mating graph is degenerate.
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EXAMPLE
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A cycle with 4 vertices is a non-mating graph. In the standard ordering of vertices, vertices 1 and 3 are both connected to vertices 2 an 4, thus having an identical sets of neighbors.
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MATHEMATICA
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k = {}; For[i = 1, i < 8, i++, lg = ListGraphs[i] ; len = Length[lg]; k = Append[k, Length[Select[Range[len], Length[Union[ToAdjacencyMatrix[lg[[ # ]]]]] != i &]]]]; k
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CROSSREFS
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Sequence in context: A079391 A162058 A113844 this_sequence A007869 A118476 A144557
Adjacent sequences: A141577 A141578 A141579 this_sequence A141581 A141582 A141583
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KEYWORD
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nonn
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AUTHOR
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Tanya Khovanova (tanyakh(AT)yahoo.com), Aug 19 2008
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EXTENSIONS
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Extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 12 2008
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