Characterization of the geodesic distance on infinite graphs - UTU Research Portal

A1 Refereed original research article in a scientific journal

Characterization of the geodesic distance on infinite graphs

Authors: Dovgoshey, Oleksiy

Publisher: Utilitas Mathematica Publishing

Publication year: 2025

Journal: Utilitas Mathematica

Journal name in source: Utilitas Mathematica

Volume: 122

First page : 65

Last page: 80

ISSN: 0315-3681

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

Web address : https://doi.org/10.61091/um122-05

Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/491310530

Abstract

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.

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Funding information in the publication:
The author was supported by grant 359772 of the Academy of Finland.