

A000171


Number of selfcomplementary graphs with n nodes.
(Formerly M0014 N0780)


9



1, 0, 0, 1, 2, 0, 0, 10, 36, 0, 0, 720, 5600, 0, 0, 703760, 11220000, 0, 0, 9168331776, 293293716992, 0, 0, 1601371799340544, 102484848265030656, 0, 0, 3837878966366932639744, 491247277315343649710080, 0, 0
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OFFSET

1,5


COMMENTS

a(n) = A007869(n)A054960(n), where A007869(n) is number of unlabeled graphs with n nodes and an even number of edges and A054960(n) is number of unlabeled graphs with n nodes and an odd number of edges.


REFERENCES

Gibbs, Richard A. Selfcomplementary graphs. J. Combinatorial Theory Ser. B 16 (1974), 106123. MR0347686 (50 #188).  N. J. A. Sloane, Mar 27 2012
F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 139, Table 6.1.1.
R. C. Read, On the number of selfcomplementary graphs and digraphs, J. London Math. Soc., 38 (1963), 99104.
R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
D. Wille, Enumeration of selfcomplementary structures, J. Comb. Theory B 25 (1978) 143150.


LINKS

Table of n, a(n) for n=1..31.
H. Fripertinger, Selfcomplementary graphs
Eric Weisstein's World of Mathematics, SelfComplementary Graph


FORMULA

a(4n) = A003086(2n).


MATHEMATICA

<<Combinatorica`; Table[GraphPolynomial[n, x]/.x > 1, {n, 1, 20}] (* Geoffrey Critzer, Oct 21 2012 *)


CROSSREFS

Cf. A047660, A051251, A047832.
Cf. A008406 (triangle of coefficients of the "graph polynomial").
Sequence in context: A010893 A181501 A213704 * A054922 A231031 A061848
Adjacent sequences: A000168 A000169 A000170 * A000172 A000173 A000174


KEYWORD

nonn,nice


AUTHOR

N. J. A. Sloane.


EXTENSIONS

More terms from R. C. Read (rcread(AT)math.uwaterloo.ca) and Vladeta Jovovic.


STATUS

approved



