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
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
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Apr 03 2001
STATUS
approved