A232700
Number of labeled connected point-determining bipartite graphs on n vertices.
Original entry on oeis.org
1, 1, 0, 12, 60, 1320, 26880, 898800, 40446000, 2568736800, 225962684640, 27627178692960, 4686229692144000, 1104514965434200320, 361988888631722352000, 165271302775469812521600, 105278651889065640047462400, 93750696652129931568573619200
Offset: 1
Consider n = 4. There are 12 connected point-determining bipartite graphs on 4 vertices: the graph *--*--*--*, with 12 possible labelings. - _Justin M. Troyka_, Nov 27 2013
- Andrew Howroyd, Table of n, a(n) for n = 1..100 (terms 1..20 from Justin M. Troyka)
- Ira Gessel and Ji Li, Enumeration of point-determining graphs, arXiv:0705.0042 [math.CO], 2007-2009.
- Andy Hardt, Pete McNeely, Tung Phan, and Justin M. Troyka, Combinatorial species and graph enumeration, arXiv:1312.0542 [math.CO], 2013.
Cf.
A006024,
A004110 (labeled and unlabeled point-determining graphs).
Cf.
A092430,
A004108 (labeled and unlabeled connected point-determining graphs).
Cf.
A232699,
A218090 (labeled and unlabeled point-determining bipartite graphs).
Cf.
A088974 (unlabeled connected point-determining bipartite graphs).
-
terms = 18;
G[x_] = Sqrt[Sum[((1 + x)^2^k*Log[1 + x]^k)/k!, {k, 0, terms+1}]] + O[x]^(terms+1);
A[x_] = x + Log[1 + (G[x] - x - 1)/(1 + x)];
(CoefficientList[A[x], x]*Range[0, terms]!) // Rest (* Jean-François Alcover, Sep 13 2018, after Andrew Howroyd *)
-
seq(n)={my(A=log(1+x+O(x*x^n))); my(p=sqrt(sum(k=0, n, exp(2^k*A)*A^k/k!))); Vec(serlaplace(x + log(1+(p-x-1)/(1+x))))} \\ Andrew Howroyd, Sep 09 2018
A088974
Number of (nonisomorphic) connected bipartite graphs with minimum degree at least 2 and with n vertices.
Original entry on oeis.org
0, 0, 0, 1, 1, 5, 9, 45, 160, 1018, 6956, 67704, 830392, 13539344, 288643968, 8112651795, 300974046019, 14796399706863, 967194378235406, 84374194347669628, 9856131011755992817, 1546820212559671605395
Offset: 1
Felix Goldberg (felixg(AT)tx.technion.ac.il), Oct 30 2003
Consider n = 4. There is one connected bipartite graph with minimum degree at least 2: the square graph. Also there is one connected point-determining bipartite graph: the graph *--*--*--*. - _Justin M. Troyka_, Nov 27 2013
Cf.
A006024,
A004110 (labeled and unlabeled point-determining graphs [the latter is also unlabeled graphs w/ min. degree >= 2]).
Cf.
A059167 (labeled graphs w/ min. degree >= 2).
Cf.
A092430,
A004108 (labeled and unlabeled connected point-determining graphs [the latter is also unlabeled connected graphs w/ min. degree >= 2]).
Cf.
A059166 (labeled connected graphs w/ min. degree >= 2).
Cf.
A232699,
A218090 (labeled and unlabeled point-determining bipartite graphs).
Cf.
A232700 (labeled connected point-determining bipartite graphs).
A218090
Number of unlabeled point-determining bipartite graphs on n vertices.
Original entry on oeis.org
1, 1, 1, 1, 2, 3, 8, 17, 63, 224, 1248, 8218, 75992, 906635, 14447433, 303100595, 8415834690, 309390830222, 15105805368214, 982300491033887
Offset: 0
Consider n = 3. The triangle graph is point-determining, but it is not bipartite, so it is not counted in a(3). The graph *--*--* is bipartite, but it is not point-determining (the vertices on the two ends have the same neighborhood), so it is also not counted in a(3). The only graph counted in a(3) is the graph *--* *. - _Justin M. Troyka_, Nov 27 2013
Cf.
A006024,
A004110 (labeled and unlabeled point-determining graphs).
Cf.
A092430,
A004108 (labeled and unlabeled connected point-determining graphs).
Cf.
A232699 (labeled point-determining bipartite graphs).
Cf.
A232700,
A088974 (labeled and unlabeled connected point-determining bipartite graphs).
Showing 1-3 of 3 results.
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