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 A079565 Number of unlabeled and connected graphs on n vertices which are either bipartite or co-bipartite. 1
 1, 1, 2, 6, 16, 49, 129, 481, 1845, 9506, 57896, 463909, 4769436, 65179170, 1187099045, 29082860878, 960963147303, 42920936851975, 2594399793419459, 212465886865393053, 23596018831885668391, 3557502387712889568013, 728850489548729072323085 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS G is bipartite iff the vertices can be partitioned into two sets such that all the edges in the graph go from one of these sets to the other. G is cobipartite iff the complement of G is bipartite. For n >= 5, no graph can be both bipartite and co-bipartite. - Falk Hüffner, Jan 22 2016 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..50 FORMULA For n >= 5, a(n) = A079571(n) + A005142(n). - Falk Hüffner, Jan 22 2016 EXAMPLE Let G be a graph with 5 vertices, 4 of which form a path and the 5th adjacent only to the two vertices in the middle of the path. Then G is not bipartite nor cobipartite because there is a triangle in both G and its complement. MATHEMATICA A005142 = Import["https://oeis.org/A005142/b005142.txt", "Table"][[All, 2]]; A033995 = Import["https://oeis.org/A033995/b033995.txt", "Table"][[All, 2]]; a[n_] := If[n<5, {1, 1, 2, 6}[[n]], A005142[[n+1]] + A033995[[n+1]] - Floor[n/2]]; a /@ Range[1, 50] (* Jean-François Alcover, Sep 17 2019 *) CROSSREFS Cf. A005142, A079571. Sequence in context: A272411 A151528 A132803 * A052890 A052814 A192401 Adjacent sequences: A079562 A079563 A079564 * A079566 A079567 A079568 KEYWORD nonn AUTHOR Jim Nastos, Jan 24 2003 EXTENSIONS More terms using formula by Falk Hüffner, Jan 22 2016 Terms a(21) and beyond from Andrew Howroyd, Sep 05 2018 STATUS approved

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Last modified October 3 10:11 EDT 2023. Contains 365859 sequences. (Running on oeis4.)