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 A141580 Number of unlabeled non-mating graphs with n vertices. 7
 0, 1, 2, 6, 18, 78, 456, 4299, 68754, 1990286, 106088988, 10454883132, 1904236651216, 641859005526860, 401547534010157680, 467956331904669136874, 1019785644052109276678788, 4171197546082606538129623140 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS 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. Also the number of unlabeled graphs with n vertices and at least one endpoint. - Gus Wiseman, Sep 11 2019 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..50 Ronald C. Read, The enumeration of mating-type graphs, Report CORR 89-38, Dept. Combinatorics and Optimization, Univ. Waterloo, 1989. FORMULA a(n) = A000088(n) - A004110(n). EXAMPLE 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. From Gus Wiseman, Sep 11 2019: (Start) Non-isomorphic representatives of the a(2) = 1 through a(5) non-mating graph edge-sets:   {12}  {12}     {12}           {12}         {13,23}  {12,34}        {12,34}                  {13,23}        {13,23}                  {13,24,34}     {12,35,45}                  {14,24,34}     {13,24,34}                  {14,23,24,34}  {14,24,34}                                 {12,34,35,45}                                 {13,24,35,45}                                 {14,23,24,34}                                 {14,25,35,45}                                 {15,25,35,45}                                 {12,25,34,35,45}                                 {14,25,34,35,45}                                 {15,23,24,35,45}                                 {15,25,34,35,45}                                 {13,24,25,34,35,45}                                 {15,24,25,34,35,45}                                 {15,23,24,25,34,35,45} (End) MATHEMATICA 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 CROSSREFS The labeled version is A327379. Cf. A000088, A004110, A028242, A059167, A245797, A327335, A327371. Sequence in context: A162058 A113844 A266858 * A007869 A263915 A144557 Adjacent sequences:  A141577 A141578 A141579 * A141581 A141582 A141583 KEYWORD nonn AUTHOR Tanya Khovanova, Aug 19 2008 EXTENSIONS Extended by R. J. Mathar, Sep 12 2008 STATUS approved

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Last modified April 11 16:42 EDT 2021. Contains 342888 sequences. (Running on oeis4.)