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Paper Information

Journal:   IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI)   2014 , Volume 9 , Number 1; Page(s) 43 To 51.
 
Paper: 

ON THE GRAPHS RELATED TO GREEN RELATIONS OF FINITE SEMIGROUPS

 
 
Author(s):  GHARIBKHAJEH A.*, DOOSTIE H.
 
* DEPARTMENT OF MATHEMATICSE, SCIENCE AND RESEARCH BRANCH, ISLAMIC AZAD UNIVERSITY, TEHRAN, IRAN
 
Abstract: 

In this paper we develop an analog of the notion of the conjugacy graph of finite groups for the finite semigroups by considering the Green relations of a finite semigroup. More precisely, by defining the new graphs ΓL (S), ΓR (S), ΓH (S), ΓJ (S) and ΓD (S) (we name them the Green graphs) related to the Green relations L, R, J, H and D of a finite semigroup S, we first attempt to prove that the graphs ΓL (S) and ΓH (S) have exactly one connected component, and this graphs for regular semigroups are complete. Next, we give a necessary condition for a finite semigroup to be regular. This study shows an intrinsic difference 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.

 
Keyword(s): CONJUGACY GRAPH, REGULAR SEMIGROUP, GREEN RELATIONS
 
 
References: 
 
Click to Cite.
APA: Copy

GHARIBKHAJEH, A., & DOOSTIE, H. (2014). ON THE GRAPHS RELATED TO GREEN RELATIONS OF FINITE SEMIGROUPS. IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI), 9(1), 43-51. https://www.sid.ir/en/journal/ViewPaper.aspx?id=402230



Vancouver: Copy

GHARIBKHAJEH A., DOOSTIE H.. ON THE GRAPHS RELATED TO GREEN RELATIONS OF FINITE SEMIGROUPS. IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI). 2014 [cited 2021May12];9(1):43-51. Available from: https://www.sid.ir/en/journal/ViewPaper.aspx?id=402230



IEEE: Copy

GHARIBKHAJEH, A., DOOSTIE, H., 2014. ON THE GRAPHS RELATED TO GREEN RELATIONS OF FINITE SEMIGROUPS. IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI), [online] 9(1), pp.43-51. Available: https://www.sid.ir/en/journal/ViewPaper.aspx?id=402230.



 
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