On the Cayley D-saturated property of completely regular semigroups

In this note we study D-saturated property of completely regular semigroups. Since completely regular semigroups are semilattices of completely simple semigroups, first we characterize Cayley graphs of completely simple semigroups and the Cayley D-saturated property of these semigroups. Then we present the relation between the Cayley D-saturated property of semilattice of semigroups and the Cayley D-saturated property of its factors.