Characterization of the geodesic distance on infinite graphs - UTU Tutkimustietojärjestelmä

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Characterization of the geodesic distance on infinite graphs

Tekijät: Dovgoshey, Oleksiy

Kustantaja: Utilitas Mathematica Publishing

Julkaisuvuosi: 2025

Journal: Utilitas Mathematica

Tietokannassa oleva lehden nimi: Utilitas Mathematica

Vuosikerta: 122

Aloitussivu: 65

Lopetussivu: 80

ISSN: 0315-3681

DOI: https://doi.org/10.61091/um122-05

Verkko-osoite: https://doi.org/10.61091/um122-05

Rinnakkaistallenteen osoite: https://research.utu.fi/converis/portal/detail/Publication/491310530

Tiivistelmä

Let G be a connected graph and let d_G be the geodesic distance on V (G). The metric spaces
(V (G), d_G) were characterized up to isometry for all finite connected G by David C. Kay and Gary
Chartrand in 1965. The main result of this paper expands this characterization on innite connected
graphs. We also prove that every metric space with integer distances between its points admits an
isometric embedding in (V (G), d_G) for suitable G.

Ladattava julkaisu

This is an electronic reprint of the original article.
This reprint may differ from the original in pagination and typographic detail. Please cite the original version.

Characterization-of-the-geodesic-distance-on-infinite-graphs.pdf

Julkaisussa olevat rahoitustiedot:
The author was supported by grant 359772 of the Academy of Finland.