Proceedings of the International Geometry Center

ISSN-print: 2072-9812
ISSN-online: 2409-8906
ISO: 26324:2012
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Forbidden four cycle, star graphs and isometric embeddings

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Oleksiy Dovgoshey
http://orcid.org/0000-0001-9689-2303
Olga Rovenska
http://orcid.org/0000-0003-1612-5409

Abstract

We prove the necessary and sufficient conditions under which ultrametric spaces of arbitrary infinite cardinality admit isometric embeddings into ultrametric spaces generated by labeled star graphs.

Keywords:
Complete multipartite graph, diametrical graph, discrete ultrametric space, four-point condition, labeled star graph

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How to Cite
Dovgoshey, O., & Rovenska, O. (2026). Forbidden four cycle, star graphs and isometric embeddings. Proceedings of the International Geometry Center, 18(3), 306-331. https://doi.org/10.15673/pigc.v18i3.3268
Section
Papers
Author Biographies

Oleksiy Dovgoshey, Institute of Applied Mathematics and Mechanics of NASU, University of Turku

Department of Function Theory, Institute of Applied Mathematics and Mechanics of NASU, Slovyansk, Ukraine
Department of Mathematics and Statistics, University of Turku, Turku, Finland

Olga Rovenska, Donbas state engineering academy

Department of mathematics and modelling, Donbas state engineering academy, Kramatorsk, Ukraine