Ultrametric spaces generated by labeled star graphs
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912217330352128 |
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| author | Dovgoshey, Oleksiy Rovenska, Olga |
| author_facet | Dovgoshey, Oleksiy Rovenska, Olga |
| contents | For arbitrary star graph $S$ with a non-degenerate vertex labeling $l\colon V(S) \to \mathbb{R}^+$ we denote by $d_l$ the corresponding ultrametric on the vertex set $V(S)$ of $S$. We characterize the class $\bf US$ of all ultrametric spaces $(V(S), d_l)$ up to isometry. We also find the necessary and sufficient conditions under which the group of all self-isometries of ultrametric space $(V(S), d_l)$ coincides with the group of all self-isomorphisms of the labeled star graph $S(l)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01260 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ultrametric spaces generated by labeled star graphs Dovgoshey, Oleksiy Rovenska, Olga General Topology Primary 54E35, Secondary 54E4 For arbitrary star graph $S$ with a non-degenerate vertex labeling $l\colon V(S) \to \mathbb{R}^+$ we denote by $d_l$ the corresponding ultrametric on the vertex set $V(S)$ of $S$. We characterize the class $\bf US$ of all ultrametric spaces $(V(S), d_l)$ up to isometry. We also find the necessary and sufficient conditions under which the group of all self-isometries of ultrametric space $(V(S), d_l)$ coincides with the group of all self-isomorphisms of the labeled star graph $S(l)$. |
| title | Ultrametric spaces generated by labeled star graphs |
| topic | General Topology Primary 54E35, Secondary 54E4 |
| url | https://arxiv.org/abs/2502.01260 |