Graphs, regarded as grammar forms as well as coloring specifications, induce graph-families, so-called color-families. It can be shown that for each color-family a unique (vertex) minimal graph exists. In this paper an operation on such minimal graphs is presented. As a main result it is shown that in a minimal graph G with m vertices, none of them adjacent to all other vertices, cliques have less than m vertices and this bound cannot be improved.
