  Information about the number of Feynman graphs for a given physical process
in a given field theory is especially useful for confirming the result of a
Feynman graph generator used in an automatic system of perturbative
calculations. A method of counting the number of Feynman graphs with weight of
symmetry factor was established based on zero-dimensional field theory, and was
used in scalar theories and QED. In this article this method is generalized to
more complicated models by direct calculation of generating functions on a
symbolic calculating system. This method is applied to QCD with and without
counter terms, where many higher order are being calculated automatically.
