A060580 Number of homeomorphically irreducible general graphs on 5 labeled nodes and with n edges.

1, 10, 40, 185, 765, 2845, 10220, 33885, 105185, 305465, 830811, 2119875, 5091525, 11565505, 24977315, 51552005, 102175360, 195301015, 361365695, 649360880, 1136438375, 1941722170, 3245874555, 5318438260, 8555568895, 13531506921

Offset

0,2

Comments

A homeomorphically irreducible general graph is a graph with multiple edges and loops and without nodes of degree 2.

References

I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983.

Links

Table of n, a(n) for n=0..25.

V. Jovovic, Generating functions for homeomorphically irreducible general graphs on n labeled nodes

V. Jovovic, Recurrences for the numbers of homeomorphically irreducible general graphs on m labeled nodes and n edges

Formula

G.f.: - (5*x^22 - 20*x^21 + 23*x^20 - 815*x^19 + 8110*x^18 - 37255*x^17 + 104890*x^16 - 204469*x^15 + 296720*x^14 - 337455*x^13 + 310150*x^12 - 229885*x^11 + 131054*x^10 - 50485*x^9 + 6490*x^8 + 7255*x^7 - 6730*x^6 + 3242*x^5 - 995*x^4 + 180*x^3 - 5*x^2 - 5*x + 1)/(x - 1)^15. E.g.f. for homeomorphically irreducible general graphs with n nodes and k edges is (1 + x*y)^( - 1/2)*exp( - x*y/2 + x^2*y^2/4)*Sum_{k >= 0} 1/(1 - x)^binomial(k + 1, 2)*exp( - x^2*y*k^2/(2*(1 + x*y)) - x^2*y*k/2)*y^k/k!.

Crossrefs

Cf. A003514, A060516, A060533-A060537, A060576-A060581.

Sequence in context: A279219 A002066 A061991 * A118266 A054885 A000449

Adjacent sequences: A060577 A060578 A060579 * A060581 A060582 A060583

Keyword

easy,nonn

Author

Vladeta Jovovic, Apr 03 2001

Status

approved