A graphical difference between the inverse and regular semigroups

In this paper we investigate the Green graphs for the regular and inverse semigroups by considering the Green classes of them. And by using the properties of these semigroups, we prove that all of the five Green graphs for the inverse semigroups are isomorphic complete graphs, while this doesn''t hold for the regular semigroups. In other words, we prove that in a regular semigroup $S$ two Green graph $Gamma_{mathcal{L}}(S)$ and $Gamma_{mathcal{H}}(S)$ are isomorphic, however, the other three Green graphs are non-isomorphic to them.