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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2505.21272 |
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| _version_ | 1866912398153089024 |
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| author | O'Reilly-Regueiro, Eugenia Zapata-Fonseca, Octavio B. |
| author_facet | O'Reilly-Regueiro, Eugenia Zapata-Fonseca, Octavio B. |
| contents | This paper was inspired by a paper by Blokhuis and Brouwer [Designs, Codes and Cryptography 65, 2012] in which a definition of a graph on the flags of a biplane is given, and they prove that the graph corresponding to the unique $(11,5,2)$-biplane is determined by its spectrum. It is also inspired by the different definition of flag-graph seen in the context of maps and abstract polytopes. Here we use this definition for $(v,k,λ)$-BIBDs, and prove that if the design is symmetric then the graph is quasi-strongly regular. We will also use the definition given by Blokhuis and Brouwer for the case of biplanes and prove that this too, is a QSRG, (with different parameters). We investigate whether these graphs are determined by their spectra for some of the known biplanes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_21272 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quasi-strongly regular graphs on the flags of symmetric designs O'Reilly-Regueiro, Eugenia Zapata-Fonseca, Octavio B. Combinatorics 05B05 This paper was inspired by a paper by Blokhuis and Brouwer [Designs, Codes and Cryptography 65, 2012] in which a definition of a graph on the flags of a biplane is given, and they prove that the graph corresponding to the unique $(11,5,2)$-biplane is determined by its spectrum. It is also inspired by the different definition of flag-graph seen in the context of maps and abstract polytopes. Here we use this definition for $(v,k,λ)$-BIBDs, and prove that if the design is symmetric then the graph is quasi-strongly regular. We will also use the definition given by Blokhuis and Brouwer for the case of biplanes and prove that this too, is a QSRG, (with different parameters). We investigate whether these graphs are determined by their spectra for some of the known biplanes. |
| title | Quasi-strongly regular graphs on the flags of symmetric designs |
| topic | Combinatorics 05B05 |
| url | https://arxiv.org/abs/2505.21272 |