@article { author = {Gharibkhajeh, Ayoub and Doostie, Hossein}, title = {A graphical difference between the inverse and regular semigroups}, journal = {Bulletin of the Iranian Mathematical Society}, volume = {40}, number = {2}, pages = {413-421}, year = {2014}, publisher = {Iranian Mathematical Society (IMS)}, issn = {1017-060X}, eissn = {1735-8515}, doi = {}, abstract = {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. }, keywords = {Regular and inverse semigroup,Green relations,Green graphs}, url = {http://bims.iranjournals.ir/article_505.html}, eprint = {http://bims.iranjournals.ir/article_505_8d4a7f029daec49b029448a7f5252b20.pdf} }