Degree 2 transformation semigroups as continuous maps on graphs: Foundations and structure

We develop the theory of transformation semigroups that have degree 2, is, act by partial functions on a finite set such inverse image points at most two elements. show graph fibers an action gives deep connection between semigroup and theory. It is known Krohn–Rhodes complexity 2 2. monoid continuous maps translational hull appropriate 0-simple semigroup. how group mapping can be considered as regular covers their right letter relate this to fibers.