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A033995
Number of bipartite graphs with n nodes.
25
1, 1, 2, 3, 7, 13, 35, 88, 303, 1119, 5479, 32303, 251135, 2527712, 33985853, 611846940, 14864650924, 488222721992, 21712049275198, 1308300679611469, 106897965189674291, 11852113048215107822, 1784730721403509209215, 365323537513403184463273
OFFSET
0,3
COMMENTS
All bipartite graphs are perfect. - Falk Hüffner, Nov 27 2015
EULER transform of A005142 [1, 1, 1, 3, 5, 17, ...] is [1, 2, 3, 7, 13, ...]. - Michael Somos, May 13 2019
REFERENCES
R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.
LINKS
CombOS - Combinatorial Object Server, Generate graphs.
P. Erdős, D. J. Kleitman, and B. L. Rothschild, Asymptotic enumeration of k_n-free graphs. In Colloquio Internazionale sulle Teorie Combinatorie, (Rome, 1973), Tomo II, Atti dei Convegni Lincei, No. 17, pp. 19-27. Accad. Naz. Lincei, Rome.
P. Hanlon, The enumeration of bipartite graphs, Discrete Math. 28 (1979), 49-57.
S. Hougardy, Home Page.
S. Hougardy, Classes of perfect graphs, Discr. Math. 306 (2006), 2529-2571.
Eric Weisstein's World of Mathematics, Bipartite Graph.
Eric Weisstein's World of Mathematics, Bicolorable Graph.
Eric Weisstein's World of Mathematics, n-Colorable Graph.
EXAMPLE
For n=1: o; n=2: o o, o-o; n=3: o o o, o o-o, o-o-o; n=4: o o o o, o o o-o, o-o o-o, o o-o-o, o-o-o-o, K_{2,2}, K_{3,1}. - Michael Somos, May 13 2019
MATHEMATICA
A005142 = Cases[Import["https://oeis.org/A005142/b005142.txt", "Table"], {_, _}][[All, 2]];
(* EulerTransform is defined in A005195 *)
EulerTransform[Rest @ A005142] (* Jean-François Alcover, Mar 18 2020 *)
CROSSREFS
Row sums of A297877.
The labeled version is A047864.
Equals A076278(n) + 1.
Cf. A005142 (connected).
Sequence in context: A045611 A006840 A123408 * A345247 A373894 A013917
KEYWORD
nonn,nice
AUTHOR
Ronald C. Read
EXTENSIONS
a(0)=1 prepended and terms a(21) and beyond from Andrew Howroyd, Sep 05 2018
STATUS
approved