A graph is called point-determining (or mating type) if no two vertices have the same neighborhood. An arbitrary graph can be reduced to a point-determining graph by contracting each set of vertices with the same neighborhood to a single vertex, and this decomposition enables us to give a simple exponential generating function for counting point-determining graphs, as accomplished by Ronald Read in 1989. In this talk we will discuss a closely related problem: counting graphs in which no two vertices have complementary neighborhoods. The decomposition approach does not work here. Instead we apply inclusion-exclusion, similarly to its use in rook theory, to obtain a simple exponential generating function for these graphs. We also discuss how this application of inclusion-exclusion is related to Möbius inversion, and how it can be applied to some related problems.