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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.15656 |
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| _version_ | 1866912594558713856 |
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| author | Preenu, C S Indu, R S George, Sijo |
| author_facet | Preenu, C S Indu, R S George, Sijo |
| contents | The principal left ideal graph of a semigroup is a simple graph whose vertices are the non-zero elements of the semigroup, and two vertices are adjacent if their principal left ideals intersect non-trivially. In this paper, we study the structure of the principal ideal graphs of inverse semigroups, particularly symmetric inverse semigroups. We also introduce the concept of skeletal of a graph and show that the principal ideal graph of an inverse semigroup has a skeletal, which is a simple graph with vertex set as $\mathcal{L}$ classes of non-zero elements. It is also proved that the principal ideal graph of symmetric inverse semigroups has a skeletal which is isomorphic to the intersection graph on the power set of a non-empty set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_15656 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the structure and skeletals of principal ideal graphs of inverse semigroups Preenu, C S Indu, R S George, Sijo Group Theory Combinatorics The principal left ideal graph of a semigroup is a simple graph whose vertices are the non-zero elements of the semigroup, and two vertices are adjacent if their principal left ideals intersect non-trivially. In this paper, we study the structure of the principal ideal graphs of inverse semigroups, particularly symmetric inverse semigroups. We also introduce the concept of skeletal of a graph and show that the principal ideal graph of an inverse semigroup has a skeletal, which is a simple graph with vertex set as $\mathcal{L}$ classes of non-zero elements. It is also proved that the principal ideal graph of symmetric inverse semigroups has a skeletal which is isomorphic to the intersection graph on the power set of a non-empty set. |
| title | On the structure and skeletals of principal ideal graphs of inverse semigroups |
| topic | Group Theory Combinatorics |
| url | https://arxiv.org/abs/2509.15656 |