Graph Representations of a Free Clifford Monoid and a Free Semilattice with Identity

The following conclusion is shown that a free Clifford monoid C_X on X is isomorphic to a monoid \overlineB_X obtained by a subset of B_X, which is the set of all birooted word trees on the same X, together with a new multiplication. Furthermore, the relation between B_X and \overlineB_X is considered. Also, it is shown that there is an isomorphism from a free semilattice with identity Y_X on X onto a monoid \overlineT_X obtained by a subset of T_X, which is the set of rooted word trees on the same X.