Ultrametric spaces generated by labeled star graphs
: Dovgoshey, Oleksiy; Rovenska, Olga
Publisher: Springer Science and Business Media LLC
: 2025
: Journal of Mathematical Sciences
: Journal of Mathematical Sciences
: 288
: 2
: 182
: 198
: 1072-3374
: 1573-8795
DOI: https://doi.org/10.1007/s10958-025-07676-6(external)
: https://doi.org/10.1007/s10958-025-07676-6(external)
: https://arxiv.org/abs/2502.01260(external)
For an arbitrary star graph S with a non-degenerate vertex labeling l : V (S) → R+, we denote
by dl the corresponding ultrametric on the vertex set V (S) of S. We characterize the class US of all
ultrametric spaces (V (S), dl) up to isometry. We also find the necessary and sufficient conditions under
which the group of all self-isometries of ultrametric space (V (S), dl) coincides with the group of all selfisomorphisms of the labeled star graph S(l).
2010 MSC. Primary 54E35, Secondary 54E4.
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The first author was supported by grant 359772 of the Academy of Finland.