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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 triangle-free 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), 49-57.

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, n-Chromatic Graph

Eric Weisstein's World of Mathematics, n-Colorable 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

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Last modified November 19 10:44 EST 2017. Contains 294936 sequences.