%0 Journal Article
%A Gharibkhajeh, A.
%A Doostie, H.
%T On the Graphs Related to Green Relations of Finite Semigroups
%J Iranian Journal of Mathematical Sciences and Informatics
%V 9
%N 1
%U http://ijmsi.ir/article-1-573-en.html
%R 10.7508/ijmsi.2014.01.004
%D 2014
%K Conjugacy graph, Regular semigroup, Green relations.,
%X 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.
%> http://ijmsi.ir/article-1-573-en.pdf
%P 43-51
%& 43
%!
%9 Research paper
%L A-10-745-1
%+
%G eng
%@ 1735-4463
%[ 2014