

A005142


Number of connected bipartite graphs with n nodes.
(Formerly M2501)


23



1, 1, 1, 1, 3, 5, 17, 44, 182, 730, 4032, 25598, 212780, 2241730, 31193324, 575252112, 14218209962, 472740425319, 21208887576786, 1286099113807999, 105567921675718772
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,5


COMMENTS

Also, the number of unlabeled connected bicolored graphs having n nodes; the color classes may be interchanged.  Robert W. Robinson
Also, for n>1, number of connected trianglefree graphs on n nodes with chromatic number 2.  Keith M. Briggs, Mar 21 2006 (cf. A116079).
Also, first diagonal of triangle in A126736.


REFERENCES

R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.
R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

Table of n, a(n) for n=0..20.
Keith M. Briggs, Combinatorial Graph Theory
P. Hanlon, The enumeration of bipartite graphs, Discrete Math. 28 (1979), 4957.
Peter Steinbach, Field Guide to Simple Graphs, Volume 1, Part 17 (For Volumes 1, 2, 3, 4 of this book see A000088, A008406, A000055, A000664, respectively.)
Eric Weisstein's World of Mathematics, Bipartite Graph.
Eric Weisstein's World of Mathematics, nChromatic Graph
Eric Weisstein's World of Mathematics, nColorable Graph


CROSSREFS

Cf. A033995, A116079.
Sequence in context: A001572 A236458 A131342 * A165452 A106063 A215106
Adjacent sequences: A005139 A005140 A005141 * A005143 A005144 A005145


KEYWORD

nonn,nice,more


AUTHOR

N. J. A. Sloane.


EXTENSIONS

More terms from R. C. Read (rcread(AT)math.uwaterloo.ca).
a(0)=1 prepended by Max Alekseyev, Jun 24 2013


STATUS

approved



