Volume 9, Issue 1 (5-2014)                   IJMSI 2014, 9(1): 43-51 | Back to browse issues page

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Gharibkhajeh A, Doostie H. On the Graphs Related to Green Relations of Finite Semigroups. IJMSI. 2014; 9 (1) :43-51
URL: http://ijmsi.ir/article-1-573-en.html

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.

Type of Study: Research | Subject: General

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