twin classes to be in a clique bundle in order that a twin class on its own is not a clique bundle and a twin class at the same time.

In a clique bundle there can be both clique classes and singleton classes but no stable set classes. In the graph shown in Figure \[fig:example\_equidom\_graph\] the clique class $\{c_1,c_2\}$ and the singleton class $\{e\}$ form a clique bundle. In Figure \[fig:cliquebundle\] you can see an equidominating graph which consists of two clique bundles. In this graph every mds contains exactly one vertex of each clique bundle.

(0,0)(21,12) (1.1,5.5)[a11]{} (2.9,5.5)[a12]{} (2,7)[a13]{}

(6,10)[a21]{} (6,8)[a22]{}

(6,4)[a31]{} (6,2)[a32]{} (5,3)[a33]{} (7,3)[a34]{}

(15,10)[b11]{} (15,8)[b12]{}

(15,4)[b21]{} (15,2)[b22]{}

(19,7)[b31]{} (19,5)[b32]{} (18,6)[b33]{} (20,6)[b34]{}

(2,6)[a1]{} (6,9)[a2]{} (6,3)[a3]{} (15,9)[b1]{} (15,3)[b2]{} (19,6)[b3]{}

(4.5,6)(5,6) (16.5,6)(5,6)

(0,1)[$\mathcal{C}_1$]{} (21,1)[$\mathcal{C}_2$]{}

We use the term *bundle* to refer to either a stable set bundle or a clique bundle. Recall that a twin class is either a stable set class, a clique class or a singleton class. Due to the existence of bundles we introduce a sort of generalization of twin classes: a *pseudo class* is either a twin class not contained in a bundle or a stable set bundle or a clique bundle. That is, a pseudo 