Topological properties of generalized Markoff mod $p$ graphs
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914221269188608 |
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| author | Satake, Shohei Yamasaki, Yoshinori |
| author_facet | Satake, Shohei Yamasaki, Yoshinori |
| contents | The generalized Markoff mod $p$ graph is defined via the equation $x^2+y^2+z^2=xyz+κ$ over the finite field $\mathbb{F}_p$ of prime order $p$. In this paper, we investigate the topological properties of the graph such as non-planarity, surface embeddability, and the existence of short cycles. Our approach is based on a systematic construction of $K_{3,3}$-subdivisions, integrating techniques from graph theory, computer algebra, and number theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21963 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Topological properties of generalized Markoff mod $p$ graphs Satake, Shohei Yamasaki, Yoshinori Number Theory Combinatorics 11D25, 05C10, 13P15 The generalized Markoff mod $p$ graph is defined via the equation $x^2+y^2+z^2=xyz+κ$ over the finite field $\mathbb{F}_p$ of prime order $p$. In this paper, we investigate the topological properties of the graph such as non-planarity, surface embeddability, and the existence of short cycles. Our approach is based on a systematic construction of $K_{3,3}$-subdivisions, integrating techniques from graph theory, computer algebra, and number theory. |
| title | Topological properties of generalized Markoff mod $p$ graphs |
| topic | Number Theory Combinatorics 11D25, 05C10, 13P15 |
| url | https://arxiv.org/abs/2512.21963 |