Name for Cayley graph of a semigroups? I did Google search and can't find a good answer. I thought I should ask experts here.

Cayley graph is defined for groups. My question is:


  Is there a special name for the Cayley graph of semigroups?
We call them Cayley graphs (it doesn't seem to be usual to say 'Cayley digraph'), and they are interesting.  I am doing research on semigroups, and quite often draw the Cayley graph of a semigroup to get an idea of what it's like.  I don't know how much background on semigroups you have, but one reason Cayley graphs for semigroups are interesting is that the $\mathcal{R}$-classes in a semigroup correspond to the strongly connected components in its (right) Cayley graph.
The difference between a semigroup and a group is the existence of an identity and inverses and it are just those properties that make Cayley graphs interesting ( read: possible ). There are no Cayley graphs for semigroups.