classes are specified to be *clique classes* in the first and *stable set classes* in the latter case. A twin class can also be a single vertex. Even though a single vertex is strictly speaking a stable set as well as a clique, we use the terms clique class and stable set class only for twin classes with at least two elements. A twin class with one vertex is called a *singleton class*. In Figure \[fig:example\_equidom\_graph\], $c_1$ and $c_2$ form a clique class, $s_1$ and $s_2$ a stable set class, and all other vertices singleton classes.

Let $T_1$ and $T_2$ be two twin classes. Then either every vertex of $T_1$ is adjacent to every vertex of $T_2$ or every vertex of $T_1$ is non-adjacent to every vertex of $T_2$. In the first case we say that $T_1$ and $T_2$ *see* each other and that $T_1$ sees $T_2$ and vice versa. We also say that a vertex and a twin class see each other, and likewise two vertices. Furthermore, if appropriate we use expressions for twin classes which are usually used for vertices (e.g. a twin class is adjacent to, dominates, is dominated by, ...).

For the sake of completeness we 