Diameter and Girth of Representation Graphs of Quadratic Forms
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866929739672846336 |
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| author | Lorenz, Nico Zimmermann, Marc Christian |
| author_facet | Lorenz, Nico Zimmermann, Marc Christian |
| contents | Let $q$ be a non-degenerate quadratic form defined on an $F$ vector space $V$ and $a \in F$. We consider the Cayley graph on $V$ with generating set $\{x \in V \mid q(x) = a\}$ and study its diameter and girth. In particular, if $F$ is a finite field, we calculate these invariants and the number of cycles of minimal length in these graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_01721 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Diameter and Girth of Representation Graphs of Quadratic Forms Lorenz, Nico Zimmermann, Marc Christian Number Theory Combinatorics Let $q$ be a non-degenerate quadratic form defined on an $F$ vector space $V$ and $a \in F$. We consider the Cayley graph on $V$ with generating set $\{x \in V \mid q(x) = a\}$ and study its diameter and girth. In particular, if $F$ is a finite field, we calculate these invariants and the number of cycles of minimal length in these graphs. |
| title | Diameter and Girth of Representation Graphs of Quadratic Forms |
| topic | Number Theory Combinatorics |
| url | https://arxiv.org/abs/2503.01721 |