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A000171 Number of self-complementary 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 (list; graph; refs; listen; history; text; internal format)
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. Self-complementary graphs. J. Combinatorial Theory Ser. B 16 (1974), 106--123. 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 self-complementary graphs and digraphs, J. London Math. Soc., 38 (1963), 99-104.

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 self-complementary structures, J. Comb. Theory B 25 (1978) 143-150.

LINKS

Table of n, a(n) for n=1..31.

H. Fripertinger, Self-complementary graphs

Eric Weisstein's World of Mathematics, Self-Complementary 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

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Last modified April 17 14:44 EDT 2014. Contains 240646 sequences.