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A000273 Number of directed graphs (or digraphs) with n nodes.
(Formerly M3032 N1229)
1, 1, 3, 16, 218, 9608, 1540944, 882033440, 1793359192848, 13027956824399552, 341260431952972580352, 32522909385055886111197440, 11366745430825400574433894004224, 14669085692712929869037096075316220928 (list; graph; refs; listen; history; text; internal format)



CRC Handbook of Combinatorial Designs, 1996, p. 651.

R. L. Davis, The numbers of structures of finite relations, Proc. Amer. Math. Soc., 4 (1953), 486-494.

J. L. Gross and J. Yellen, eds., Handbook of Graph Theory, CRC Press, 2004; p. 522.

F. Harary, Graph Theory. Addison-Wesley, Reading, MA, 1969, p. 225.

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 124, Table 5.1.2 and p. 241, Table A4.

A. Iványi, Leader election in synchronous networks, Acta Univ. Sapientiae, Mathematica, 5, 2 (2013) 54-82.

M. D. McIlroy, Calculation of numbers of structures of relations on finite sets, Massachusetts Institute of Technology, Research Laboratory of Electronics, Quarterly Progress Reports, No. 17, Sept. 15, 1955, pp. 14-22.

W. Oberschelp, Kombinatorische Anzahlbestimmungen in Relationen, Math. Ann., 174 (1967), 53-78.

J. Qian, Enumeration of unlabeled directed hypergraphs, Electronic Journal of Combinatorics, 20(1) (2013), #P46. - From N. J. A. Sloane, Mar 01 2013

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).


Keith Briggs, Table of n, a(n) for n = 0..64

R. Absil and H Mélot, Digenes: genetic algorithms to discover conjectures about directed and undirected graphs, arXiv preprint arXiv:1304.7993, 2013

P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.

G. Pfeiffer, Counting Transitive Relations, Journal of Integer Sequences, Vol. 7 (2004), Article 04.3.2.

L. Travis, [math/9811127] Graphical Enumeration: A Species-Theoretic Approach

Eric Weisstein's World of Mathematics, Directed Graph

Index entries for "core" sequences


(Maple code from Vladeta Jovovic, Jun 06 2006) with(combinat):with(numtheory):

for n from 1 to 20 do p:=partition(n):

s:=0:for k from 1 to nops(p) do

q:=convert(p[k], multiset):

for i from 1 to n do a(i):=0:od:for i from 1 to nops(q) do a(q[i][1]):=q[i][2]:od:

c:=1:ord:=1:for i from 1 to n do c:=c*a(i)!*i^a(i): if a(i)<>0 then ord:=lcm(ord, i):fi:od:

g:=0:for d from 1 to ord do if ord mod d=0 then g1:=0:for del from 1 to d do if del<=n and d mod del=0 then g1:=g1+del*a(del):fi:od:g:=g+phi(ord/d)*g1*(g1-1):fi:od:



print(n, s):



Table[CycleIndex[PairGroup[SymmetricGroup[n], Ordered], t]/.Table[t[i]->1+x^i, {i, 1, n^2}]/.{x->1}, {n, 1, 7}] (* or *)

  Table[GraphPolynomial[n, t, Directed]/.{t->1}, {n, 1, 20}]

(* Geoffrey Critzer, Mar 08 2011 *)


Sequence in context: A166860 A196562 A113597 * A071897 A182012 A013923

Adjacent sequences:  A000270 A000271 A000272 * A000274 A000275 A000276




N. J. A. Sloane


More terms from Vladeta Jovovic, Dec 14 1999



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Last modified April 1 12:43 EDT 2015. Contains 256126 sequences.