Iranian Journal of Mathematical Sciences and Informatics
مجله علوم ریاضی و انفورماتیک ایرانیان
IJMSI
Basic Sciences
http://ijmsi.ir
1
admin
1735-4463
2008-9473
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7
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8888
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en
jalali
1393
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gregorian
2014
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online
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fulltext
en
On the Graphs Related to Green Relations of Finite Semigroups
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