Incidence Gain Graphs and Generalized Quadrangles
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916595571359744 |
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| author | McCulloch, Ryan |
| author_facet | McCulloch, Ryan |
| contents | We demonstrate a construction method based on a gain function that is defined on the incidence graph of an incidence geometry. Restricting to when the incidence geometry is a linear space, we show that the construction yields a generalized quadrangle provided that the gain function satisfies a certain bijective property. Our method is valid for finite and infinite geometries. We produce a family of generalized quadrangles by defining such a gain function on an affine plane over an arbitrary field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01805 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Incidence Gain Graphs and Generalized Quadrangles McCulloch, Ryan Combinatorics Primary 05B25, Secondary 51E12 We demonstrate a construction method based on a gain function that is defined on the incidence graph of an incidence geometry. Restricting to when the incidence geometry is a linear space, we show that the construction yields a generalized quadrangle provided that the gain function satisfies a certain bijective property. Our method is valid for finite and infinite geometries. We produce a family of generalized quadrangles by defining such a gain function on an affine plane over an arbitrary field. |
| title | Incidence Gain Graphs and Generalized Quadrangles |
| topic | Combinatorics Primary 05B25, Secondary 51E12 |
| url | https://arxiv.org/abs/2502.01805 |