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<p>For an arbitrary star graph <i>S</i> with a non-degenerate vertex labeling <i>l</i>: <i>V</i> (<i>S</i>) → ℝ<sup>+</sup>, we denote by <i>d</i><sub><i>l</i></sub> the corresponding ultrametric on the vertex set <i>V</i> (<i>S</i>) of <i>S</i>. We characterize the class <b>US</b> of all ultrametric spaces (<i>V</i> (<i>S</i>), <i>d</i><sub><i>l</i></sub>) up to isometry. We also find the necessary and sufficient conditions under which the group of all self-isometries of ultrametric space (<i>V</i> (<i>S</i>), <i>d</i><sub><i>l</i></sub>) coincides with the group of all selfisomorphisms of the labeled star graph <i>S</i>(<i>l</i>).</p>

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Ultrametric spaces generated by labeled star graphs

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • Oleksiy Dovgoshey,
  • Olga Rovenska

摘要

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).