Abstract
In this paper, we give a number of illuminating examples of transformation semigroups of degree 2 acting on graphs by functions that preserve vertices and edges by inverse image. It is known that the complexity of such a transformation semigroup is at most 2. We give examples that use sophisticated lower bounds to complexity to distinguish between complexity 1 and complexity 2.
| Original language | English |
|---|---|
| Pages (from-to) | 289-316 |
| Number of pages | 28 |
| Journal | International Journal of Algebra and Computation |
| Volume | 33 |
| Issue number | 2 |
| DOIs | |
| State | Published - 1 Mar 2023 |
Bibliographical note
Publisher Copyright:© 2023 World Scientific Publishing Company.
Funding
Supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education grants NRF- 2016R1A2B4008487 and 2016R1A6A1A03010528 (S.-H.K.); and the development fund of Catholic Institute for Visual Science of 2019 grant 5-2019-B0001-00242 (J.A.C.).
| Funders | Funder number |
|---|---|
| development fund of Catholic Institute for Visual Science | 5-2019-B0001-00242 |
| National Research Foundation of Korea | |
| Kementerian Pendidikan Malaysia | 2016R1A6A1A03010528, NRF- 2016R1A2B4008487 |
Keywords
- Degree of a transformation semigroup
- complexity of semigroups