$q$-Analogs of divisible design graphs and Deza graphs
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866911883791958016 |
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| author | Crnkovic, Dean De Boeck, Maarten Pavese, Francesco Svob, Andrea |
| author_facet | Crnkovic, Dean De Boeck, Maarten Pavese, Francesco Svob, Andrea |
| contents | Divisible design graphs were introduced in 2011 by Haemers, Kharaghani and Meulenberg. In this paper, we introduce the notion of $q$-analogs of divisible design graphs and show that all $q$-analogs of divisible design graphs come from spreads, and are actually $q$-analogs of strongly regular graphs. Deza graphs were introduced by Erickson, Fernando, Haemers and Hardy in 1999. In this paper, we introduce $q$-analogs of Deza graphs. Further, we determine possible parameters, give examples of $q$-analogs of Deza graphs and characterize all non-strongly regular $q$-analogs of Deza graphs with the smallest parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_13230 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $q$-Analogs of divisible design graphs and Deza graphs Crnkovic, Dean De Boeck, Maarten Pavese, Francesco Svob, Andrea Combinatorics Divisible design graphs were introduced in 2011 by Haemers, Kharaghani and Meulenberg. In this paper, we introduce the notion of $q$-analogs of divisible design graphs and show that all $q$-analogs of divisible design graphs come from spreads, and are actually $q$-analogs of strongly regular graphs. Deza graphs were introduced by Erickson, Fernando, Haemers and Hardy in 1999. In this paper, we introduce $q$-analogs of Deza graphs. Further, we determine possible parameters, give examples of $q$-analogs of Deza graphs and characterize all non-strongly regular $q$-analogs of Deza graphs with the smallest parameters. |
| title | $q$-Analogs of divisible design graphs and Deza graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2405.13230 |