en عمومى General پژوهشي Research paper <p>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.</p> Conjugacy graph, Regular semigroup, Green relations. 43 51 http://ijmsi.ir/browse.php?a_code=A-10-745-1&slc_lang=en&sid=1 A. Gharibkhajeh a_gharib@iau-tnb.ac.ir 10031947532846002277 10031947532846002277 Yes H. Doostie doostih@gmail.com 10031947532846002278 10031947532846002278 No