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Title:On metric dimensions of hypercubes
Authors:ID Kelenc, Aleksander (Author)
ID Masa Toshi, Aoden Teo (Author)
ID Škrekovski, Riste (Author)
ID Yero, Ismael G. (Author)
Files:.pdf PDF - Presentation file, download (259,98 KB)
MD5: 471024FA77393163F7146F394B03EFFA
 
Language:English
Typology:1.01 - Original Scientific Article
Organization:Logo IMFM - Institute of Mathematics, Physics, and Mechanics
Abstract:In this note we show two unexpected results concerning the metric, the edge metric and the mixed metric dimensions of hypercube graphs. First, we show that the metric and the edge metric dimensions of Qd differ by at most one for every integer d. In particular, if d is odd, then the metric and the edge metric dimensions of Qd are equal. Second, we prove that the metric and the mixed metric dimensions of the hypercube Qd are equal for every d≥3. We conclude the paper by conjecturing that all these three types of metric dimensions of Qd are equal when d is large enough.
Keywords:edge metric dimension, mixed metric dimension, metric dimension, hypercubes
Publication status:Published
Publication version:Version of Record
Publication date:01.01.2023
Year of publishing:2023
Number of pages:art. P2.08 (9 str.)
Numbering:Vol. 23, no. 2
PID:20.500.12556/DiRROS-18477 New window
UDC:519.17
ISSN on article:1855-3966
DOI:10.26493/1855-3974.2568.55c New window
COBISS.SI-ID:140460291 New window
Note:
Publication date in DiRROS:19.03.2024
Views:770
Downloads:171
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KELENC, Aleksander, MASA TOSHI, Aoden Teo, ŠKREKOVSKI, Riste and YERO, Ismael G., 2023, On metric dimensions of hypercubes. Ars mathematica contemporanea [online]. 2023. Vol. 23, no. 2. [Accessed 7 April 2025]. DOI 10.26493/1855-3974.2568.55c. Retrieved from: https://dirros.openscience.si/IzpisGradiva.php?lang=eng&id=18477
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Record is a part of a journal

Title:Ars mathematica contemporanea
Publisher:Društvo matematikov, fizikov in astronomov, Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije
ISSN:1855-3966
COBISS.SI-ID:239049984 New window

Document is financed by a project

Funder:ARIS - Slovenian Research and Innovation Agency
Funding programme:Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije
Project number:J1-1693-2019
Name:Sodobni in novi metrični koncepti v teoriji grafov
Funder:ARIS - Slovenian Research and Innovation Agency
Funding programme:Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije
Project number:J1-2452-2020
Name:Strukturni, optimizacijski in algoritmični problemi v geometrijskih in topoloških predstavitvah grafov
Funder:ARIS - Slovenian Research and Innovation Agency
Funding programme:Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije
Project number:P1-0383-2017
Name:Kompleksna omrežja
Funder:ARIS - Slovenian Research and Innovation Agency
Funding programme:Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije
Project number:J1-3002-2021
Name:Prirejanja in barvanja povezav v kubičnih grafih

Licences

License:CC BY 4.0, Creative Commons Attribution 4.0 International
Link:http://creativecommons.org/licenses/by/4.0/
Description:This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

Language:Slovenian
Keywords:metrična dimenzija roba, mešana metrična dimenzija, metrična dimenzija, hiperkocke


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