Pseudo-Geometric Strongly Regular Graphs with a Regular Point
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866914459323203584 |
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| author | van Dam, Edwin Guo, Krystal |
| author_facet | van Dam, Edwin Guo, Krystal |
| contents | We study pseudo-geometric strongly regular graphs whose second subconstituent with respect to a vertex is a cover of a strongly regular graph or a complete graph. By studying the structure of such graphs, we characterize all graphs containing such a vertex, and use our characterization to find many new strongly regular graphs. Thereby, we answer a question posed by Gardiner, Godsil, Hensel, and Royle. We give an explicit construction for q new, pairwise non-isomorphic graphs with the same parameters as the collinearity graph of generalized quadrangles of order $(q,q)$ and a new non-geometric graph with the same parameters as the collinearity graph of the Hermitian generalized quadrangle of order $(q^2, q)$, for prime powers $q$. Using our characterization, we computed 135478 new strongly regular graphs with parameters (85,20,3,5) and 27 039 strongly regular graphs with parameters (156, 30, 4, 6). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_04755 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Pseudo-Geometric Strongly Regular Graphs with a Regular Point van Dam, Edwin Guo, Krystal Combinatorics 05E30, 51E12, 05C50 We study pseudo-geometric strongly regular graphs whose second subconstituent with respect to a vertex is a cover of a strongly regular graph or a complete graph. By studying the structure of such graphs, we characterize all graphs containing such a vertex, and use our characterization to find many new strongly regular graphs. Thereby, we answer a question posed by Gardiner, Godsil, Hensel, and Royle. We give an explicit construction for q new, pairwise non-isomorphic graphs with the same parameters as the collinearity graph of generalized quadrangles of order $(q,q)$ and a new non-geometric graph with the same parameters as the collinearity graph of the Hermitian generalized quadrangle of order $(q^2, q)$, for prime powers $q$. Using our characterization, we computed 135478 new strongly regular graphs with parameters (85,20,3,5) and 27 039 strongly regular graphs with parameters (156, 30, 4, 6). |
| title | Pseudo-Geometric Strongly Regular Graphs with a Regular Point |
| topic | Combinatorics 05E30, 51E12, 05C50 |
| url | https://arxiv.org/abs/2204.04755 |