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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2025-08-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2025-0187 |
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| Summary: | 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. |
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| ISSN: | 2391-5455 |