Green's graphs of a semigroup
Let SS be a semigroup. In this study, we first introduce the Green’s digraphs and Green’s graphs related to the Green’s relations L{\mathscr{L}}, R{\mathscr{R}}, and J{\mathscr{J}} of SS. Further, the connectedness and completeness of the Green’s graphs are discussed. For a finite semigroup SS, we s...
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| Format: | Article |
| Language: | English |
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De Gruyter
2025-08-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2025-0187 |
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| author | Cheng Yanliang Shao Yong Ma Xuanlong |
| author_facet | Cheng Yanliang Shao Yong Ma Xuanlong |
| author_sort | Cheng Yanliang |
| collection | DOAJ |
| description | Let SS be a semigroup. In this study, we first introduce the Green’s digraphs and Green’s graphs related to the Green’s relations L{\mathscr{L}}, R{\mathscr{R}}, and J{\mathscr{J}} of SS. Further, the connectedness and completeness of the Green’s graphs are discussed. For a finite semigroup SS, we show that each of the Green’s graphs of SS has a transitive orientation. Moreover, we obtain that these Green’s graphs are perfect. Finally, the structures of the Green’s graphs are characterized using the generalized lexicographic product. |
| format | Article |
| id | doaj-art-faa94d05fbdc42a088b63aa06e6716e6 |
| institution | Kabale University |
| issn | 2391-5455 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj-art-faa94d05fbdc42a088b63aa06e6716e62025-08-20T03:46:50ZengDe GruyterOpen Mathematics2391-54552025-08-0123141141810.1515/math-2025-0187Green's graphs of a semigroupCheng Yanliang0Shao Yong1Ma Xuanlong2School of Mathematics, Northwest University, Xi’an, Shaanxi, 710127, P. R. ChinaSchool of Mathematics, Northwest University, Xi’an, Shaanxi, 710127, P. R. ChinaSchool of Science, Xi’an Shiyou University, Xi’an, Shaanxi, 710065, P. R. ChinaLet SS be a semigroup. In this study, we first introduce the Green’s digraphs and Green’s graphs related to the Green’s relations L{\mathscr{L}}, R{\mathscr{R}}, and J{\mathscr{J}} of SS. Further, the connectedness and completeness of the Green’s graphs are discussed. For a finite semigroup SS, we show that each of the Green’s graphs of SS has a transitive orientation. Moreover, we obtain that these Green’s graphs are perfect. Finally, the structures of the Green’s graphs are characterized using the generalized lexicographic product.https://doi.org/10.1515/math-2025-0187semigroupgreen’s relationgreen’s graphcomplete graphconnected graph05c2520m99 |
| spellingShingle | Cheng Yanliang Shao Yong Ma Xuanlong Green's graphs of a semigroup Open Mathematics semigroup green’s relation green’s graph complete graph connected graph 05c25 20m99 |
| title | Green's graphs of a semigroup |
| title_full | Green's graphs of a semigroup |
| title_fullStr | Green's graphs of a semigroup |
| title_full_unstemmed | Green's graphs of a semigroup |
| title_short | Green's graphs of a semigroup |
| title_sort | green s graphs of a semigroup |
| topic | semigroup green’s relation green’s graph complete graph connected graph 05c25 20m99 |
| url | https://doi.org/10.1515/math-2025-0187 |
| work_keys_str_mv | AT chengyanliang greensgraphsofasemigroup AT shaoyong greensgraphsofasemigroup AT maxuanlong greensgraphsofasemigroup |