Structural properties and isomorphism theorems for Cayley digraphs of full transformation semigroups with respect to Green's equivalence classes
Let T(X) be the full transformation semigroup on a nonempty set X. In this paper, the Cayley digraphs of T(X) with connection sets L and R, the Green's equivalence classes of T(X) according to the Green's relations L and R, are investigated. Furthermore, their connectedness properties are...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-01-01
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| Series: | Heliyon |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405844023001834 |
| _version_ | 1811173362230099968 |
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| author | Nuttawoot Nupo Yanisa Chaiya |
| author_facet | Nuttawoot Nupo Yanisa Chaiya |
| author_sort | Nuttawoot Nupo |
| collection | DOAJ |
| description | Let T(X) be the full transformation semigroup on a nonempty set X. In this paper, the Cayley digraphs of T(X) with connection sets L and R, the Green's equivalence classes of T(X) according to the Green's relations L and R, are investigated. Furthermore, their connectedness properties are characterized. In addition, the isomorphism theorems for Cayley digraphs of T(X) are also presented. |
| first_indexed | 2024-04-10T17:45:34Z |
| format | Article |
| id | doaj.art-927587102dc84b0eb6b646127046bcc6 |
| institution | Directory Open Access Journal |
| issn | 2405-8440 |
| language | English |
| last_indexed | 2024-04-10T17:45:34Z |
| publishDate | 2023-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Heliyon |
| spelling | doaj.art-927587102dc84b0eb6b646127046bcc62023-02-03T04:59:59ZengElsevierHeliyon2405-84402023-01-0191e12976Structural properties and isomorphism theorems for Cayley digraphs of full transformation semigroups with respect to Green's equivalence classesNuttawoot Nupo0Yanisa Chaiya1Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, 40002, ThailandDepartment of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani, 12120, Thailand; Corresponding author.Let T(X) be the full transformation semigroup on a nonempty set X. In this paper, the Cayley digraphs of T(X) with connection sets L and R, the Green's equivalence classes of T(X) according to the Green's relations L and R, are investigated. Furthermore, their connectedness properties are characterized. In addition, the isomorphism theorems for Cayley digraphs of T(X) are also presented.http://www.sciencedirect.com/science/article/pii/S2405844023001834Cayley digraphFull transformation semigroupGreen's relationsIsomorphism theoremConnectedness |
| spellingShingle | Nuttawoot Nupo Yanisa Chaiya Structural properties and isomorphism theorems for Cayley digraphs of full transformation semigroups with respect to Green's equivalence classes Heliyon Cayley digraph Full transformation semigroup Green's relations Isomorphism theorem Connectedness |
| title | Structural properties and isomorphism theorems for Cayley digraphs of full transformation semigroups with respect to Green's equivalence classes |
| title_full | Structural properties and isomorphism theorems for Cayley digraphs of full transformation semigroups with respect to Green's equivalence classes |
| title_fullStr | Structural properties and isomorphism theorems for Cayley digraphs of full transformation semigroups with respect to Green's equivalence classes |
| title_full_unstemmed | Structural properties and isomorphism theorems for Cayley digraphs of full transformation semigroups with respect to Green's equivalence classes |
| title_short | Structural properties and isomorphism theorems for Cayley digraphs of full transformation semigroups with respect to Green's equivalence classes |
| title_sort | structural properties and isomorphism theorems for cayley digraphs of full transformation semigroups with respect to green s equivalence classes |
| topic | Cayley digraph Full transformation semigroup Green's relations Isomorphism theorem Connectedness |
| url | http://www.sciencedirect.com/science/article/pii/S2405844023001834 |
| work_keys_str_mv | AT nuttawootnupo structuralpropertiesandisomorphismtheoremsforcayleydigraphsoffulltransformationsemigroupswithrespecttogreensequivalenceclasses AT yanisachaiya structuralpropertiesandisomorphismtheoremsforcayleydigraphsoffulltransformationsemigroupswithrespecttogreensequivalenceclasses |