A060579 Number of homeomorphically irreducible general graphs on 4 labeled nodes and with n edges.

1, 6, 19, 68, 242, 704, 1981, 5140, 12364, 27614, 57598, 113108, 210812, 375606, 643646, 1066196, 1714445, 2685464, 4109493, 6158768, 9058119, 13097592, 18647371, 26175300, 36267330, 49651242, 67224024, 90083308, 119563302

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..28.

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.: (4*x^15 + 5*x^14 - 194*x^13 + 881*x^12 - 2058*x^11 + 3096*x^10 - 3330*x^9 + 2628*x^8 - 1398*x^7 + 359*x^6 + 72*x^5 - 93*x^4 + 28*x^3 + 4*x^2 - 4*x + 1)/(x - 1)^10. 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: A055916 A266472 A259804 * A183326 A123950 A100191

Adjacent sequences: A060576 A060577 A060578 * A060580 A060581 A060582

Keyword

easy,nonn

Author

Vladeta Jovovic, Apr 03 2001

Status

approved