Characterization of the geodesic distance on infinite graphs

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dc.contributor.authorDovgoshey, Oleksiy
dc.contributor.organizationfi=matematiikka|en=Mathematics|
dc.contributor.organization-code1.2.246.10.2458963.20.41687507875
dc.converis.publication-id491310530
dc.converis.urlhttps://research.utu.fi/converis/portal/Publication/491310530
dc.date.accessioned2025-08-28T02:05:32Z
dc.date.available2025-08-28T02:05:32Z
dc.description.abstract<p>Let <i>G </i>be a connected graph and let <i>d<sub>G</sub></i> be the geodesic distance on <i>V (G)</i>. The metric spaces<br>(<i>V (G), d<sub>G</sub></i>) were characterized up to isometry for all finite connected <i>G </i>by David C. Kay and Gary<br>Chartrand in 1965. The main result of this paper expands this characterization on innite connected<br>graphs. We also prove that every metric space with integer distances between its points admits an<br>isometric embedding in (<i>V (G), d<sub>G</sub></i>) for suitable <i>G</i>.<br></p>
dc.format.pagerange65
dc.format.pagerange80
dc.identifier.jour-issn0315-3681
dc.identifier.olddbid208568
dc.identifier.oldhandle10024/191595
dc.identifier.urihttps://www.utupub.fi/handle/11111/58042
dc.identifier.urlhttps://doi.org/10.61091/um122-05
dc.identifier.urnURN:NBN:fi-fe2025082788027
dc.language.isoen
dc.okm.affiliatedauthorDovgoshey, Oleksiy
dc.okm.discipline111 Mathematicsen_GB
dc.okm.discipline111 Matematiikkafi_FI
dc.okm.internationalcopublicationinternational co-publication
dc.okm.internationalityInternational publication
dc.okm.typeA1 ScientificArticle
dc.publisherUtilitas Mathematica Publishing
dc.publisher.countryCanadaen_GB
dc.publisher.countryKanadafi_FI
dc.publisher.country-codeCA
dc.relation.doi10.61091/um122-05
dc.relation.ispartofjournalUtilitas Mathematica
dc.relation.volume122
dc.source.identifierhttps://www.utupub.fi/handle/10024/191595
dc.titleCharacterization of the geodesic distance on infinite graphs
dc.year.issued2025

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