A003028
Number of digraphs on n labeled nodes with a source.
Original entry on oeis.org
1, 3, 51, 3614, 991930, 1051469032, 4366988803688, 71895397383029040, 4719082081411731363408, 1237678715644664931691596416, 1297992266840866792981316221144960, 5444416466164313011147841248189209354496, 91343356480627224177654291875698256656613808896
Offset: 1
- V. Jovovic and G. Kilibarda, Enumeration of labeled initially-finally connected digraphs, Scientific review, Serbian Scientific Society, 19-20 (1996) 237-247.
- R. W. Robinson, Counting labeled acyclic digraphs, pp. 239-273 of F. Harary, editor, New Directions in the Theory of Graphs. Academic Press, NY, 1973.
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
A049524
Number of digraphs with a source and a sink on n labeled nodes.
Original entry on oeis.org
1, 3, 48, 3424, 962020, 1037312116, 4344821892264, 71771421308713624, 4716467927380427847264, 1237465168798883061207535456, 1297923989772809185944542332007104, 5444330658513426322624322033259452670016, 91342931436147421630261703458729460990513248512
Offset: 1
- V. Jovovic, G. Kilibarda, Enumeration of labeled initially-finally connected digraphs, Scientific review, Serbian Scientific Society, 19-20 (1996), p. 244.
- Andrew Howroyd, Table of n, a(n) for n = 1..50
- Sean A. Irvine, Java program (github)
- V. Jovovic and G. Kilibarda, Enumeration of labeled quasi-initially connected digraphs, Discrete Math., 224 (2000), 151-163.
- R. W. Robinson, Counting digraphs with restrictions on the strong components, Combinatorics and Graph Theory '95 (T.-H. Ku, ed.), World Scientific, Singapore (1995), 343-354.
A003088
Number of unilateral digraphs with n unlabeled nodes.
Original entry on oeis.org
1, 1, 2, 11, 171, 8603, 1478644, 870014637
Offset: 0
- F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 218.
- Ronald C. Read, email to N. J. A. Sloane, 28 August, 2000.
- R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Note that Read and Wilson incorrectly give a(4) as 172 - thanks to
Vladeta Jovovic, Goran Kilibarda for finding this error and for verifying a(5).
A049414
Number of quasi-initially connected digraphs with n labeled nodes.
Original entry on oeis.org
1, 3, 54, 3804, 1022320, 1065957628, 4389587378792, 72020744942708040, 4721708591209396542528, 1237892622263984613044109216, 1298060581376190776821670648395840
Offset: 1
A057275
Triangle T(n,k) of number of unilaterally connected digraphs on n labeled nodes and with k arcs, k=0..n*(n-1).
Original entry on oeis.org
1, 0, 2, 1, 0, 0, 6, 20, 15, 6, 1, 0, 0, 0, 24, 222, 660, 908, 792, 495, 220, 66, 12, 1, 0, 0, 0, 0, 120, 2304, 15540, 52700, 109545, 161120, 182946, 167660, 125945, 77520, 38760, 15504, 4845, 1140, 190, 20, 1
Offset: 1
Triangle begins:
[1],
[0,2,1],
[0,0,6,20,15,6,1],
[0,0,0,0,24,222,660,908,792,495,220,66,12,1],
...
The number of unilaterally connected digraphs on 3 labeled nodes is 48 = 6+20+15+6+1.
-
\\ See A057273 for Strong.
Unilaterally(n, e=2)={my(u=vector(n), s=Strong(n,e)); for(n=1, #u, u[n]=vector(n, k, binomial(n,k)*s[k]*if(k==n, 1, sum(j=1, n-k, e^(k*(n-k-j))*(e^(k*j)-1)*u[n-k][j])))); vector(#u, n, vecsum(u[n]))}
row(n)={Vecrev(Unilaterally(n, 1+'y)[n])}
{ for(n=1, 5, print(row(n))) } \\ Andrew Howroyd, Jan 19 2022
Showing 1-5 of 5 results.
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