RT - Journal Article T1 - On the Graphs Related to Green Relations of Finite Semigroups JF - IJMSI YR - 2014 JO - IJMSI VO - 9 IS - 1 UR - http://ijmsi.ir/article-1-573-en.html SP - 43 EP - 51 K1 - Conjugacy graph K1 - Regular semigroup K1 - Green relations. AB - In this paper we develop an analog of the notion of the con- jugacy graph of  nite groups for the  nite semigroups by considering the Green relations of a  nite semigroup. More precisely, by de ning the new graphs $Gamma_{L}(S)$, $Gamma_{H}(S)$, $Gamma_{J}(S)$ and $Gamma_{D}(S)$ (we name them the Green graphs) related to the Green relations L R J H and D of a  nite semigroup S , we  first attempt to prove that the graphs $Gamma_{D}(S)$ and $Gamma_{H}(S)$ have exactly one connected component, and this graphs for regu- lar semigroups are complete. And secondly, we give a necessary condition for a  nite semigroup to be regular. This study shows an intrinsic di er- ence between the conjugacy graphs (of groups) and the Green graphs (of semigroups) as well. Finally, our calculations include two kinds of semi- groups, mostly involving the well known Lucas numbers, and examining the proved assertions. LA eng UL http://ijmsi.ir/article-1-573-en.html M3 10.7508/ijmsi.2014.01.004 ER -