Structural properties and isomorphism theorems for Cayley digraphs of full transformation semigroups with respect to Green's equivalence classes.

Let T ( X ) be the full transformation semigroup on a nonempty set X. In this paper, the Cayley digraphs of T ( X ) with connection sets L and R, the Green's equivalence classes of T ( X ) according to the Green's relations L and R , are investigated. Furthermore, their connectedness properties are characterized. In addition, the isomorphism theorems for Cayley digraphs of T ( X ) are also presented.