TY - JOUR
T1 - On the Graphs Related to Green Relations of Finite Semigroups
TT -
JF - IJMSI
JO - IJMSI
VL - 9
IS - 1
UR - http://ijmsi.ir/article-1-573-en.html
Y1 - 2014
SP - 43
EP - 51
KW - Conjugacy graph
KW - Regular semigroup
KW - Green relations.
N2 - 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.
M3 10.7508/ijmsi.2014.01.004
ER -