Abstract Let S S be a semigroup. In this study, we first introduce the Green’s digraphs and Green’s graphs related to the Green’s relations L L, R R, and J J of S S. Further, the connectedness and completeness of the Green’s graphs are discussed. For a finite semigroup S S, we show that each of the Green’s graphs of S S has a transitive orientation. Moreover, we obtain that these Green’s graphs are perfect. Finally, the structures of the Green’s graphs are characterized using the generalized lexicographic product.
Cheng et al. (Wed,) studied this question.