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.