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Information Journal Paper

Title

ON THE GRAPHS RELATED TO GREEN RELATIONS OF FINITE SEMIGROUPS

Pages

  43-51

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.

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    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. SID. https://sid.ir/paper/310375/en

    Vancouver: Copy

    GHARIBKHAJEH A., DOOSTIE H.. ON THE GRAPHS RELATED TO GREEN RELATIONS OF FINITE SEMIGROUPS. IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI)[Internet]. 2014;9(1):43-51. Available from: https://sid.ir/paper/310375/en

    IEEE: Copy

    A. GHARIBKHAJEH, and H. DOOSTIE, “ON THE GRAPHS RELATED TO GREEN RELATIONS OF FINITE SEMIGROUPS,” IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI), vol. 9, no. 1, pp. 43–51, 2014, [Online]. Available: https://sid.ir/paper/310375/en

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