The involution principle
We have evaluated
the number of graphs on v vertices
by examining a certain action of the form GYX. We shall now give
an example of the form H ´GYX, i.e. a power group action.
Afterwards we shall see how these two examples can be combined in order to
prove an existence theorem for a certain class of graphs. While
doing so we shall meet an interesting and useful counting principle which
uses suitable actions of S2, the smallest nontrivial group.
last changed: August 28, 2001