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Document Type |
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Thesis |
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Document Title |
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ON CAYLEY GRAPHS OF REGULAR SEMIGROUPS الرسم البياني كايلي لشبه الزمرة الاعتيادية |
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Subject |
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Faculty of Sciences |
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Document Language |
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Arabic |
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Abstract |
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The concept of Cayley graphs of groups was introduced in 1878 by Arthur Cayley. Kelarev and Praeger in 2003, initiated the study of Cayley graphs of semigroups. For a semigroup S with the connection set A, where A is a non empty subset of S, Cayley graph of S, Cay(S,A) is defined to be a directed graph with vertex set S and edge set E(Cay(S,A) )={(x,y),x,y ∈S:y=ax,a∈A}. One interesting question to study about Cayley graphs of semigroups is: under what conditions the Cayley graph of a semigroup is vertex transitive, that is every vertex can be mapped to any other vertex by an automorphism. Different authors have investigated this area, for example, S.Fan and Y.Zeng in 2007 gave a description of all vertex-transitive Cayley graphs of bands. In 2014, H.Liu investigated the Cayley graphs of completely simple semigroups which are vertex transitive. In this thesis we initiate a general study of Cayley graph Cay(S,S^°) of (an arbitrary) regular semigroup S with the connection set S^°, the inverse transversal of S. We also investigate the conditions for which Cay(S,S^°) is ColAut-vertex-transitive and when it has loops at each vertex. |
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Supervisor |
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Dr. Jehan Alawie Al-bar |
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Thesis Type |
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Master Thesis |
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Publishing Year |
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1439 AH
2018 AD |
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Added Date |
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Thursday, May 31, 2018 |
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Researchers
| حليمة حسن عسيري | Assiri, Halima Hassan | Researcher | Master | |
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