| Title: | On metric dimensions of hypercubes |
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| Authors: | ID Kelenc, Aleksander (Author)
ID Masa Toshi, Aoden Teo (Author)
ID Škrekovski, Riste (Author)
ID Yero, Ismael G. (Author) |
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| Files: |  amc_2568.pdf (255,81 KB)
MD5: 31109123EAFE285A7B6F399850D9AF26
 https://amc-journal.eu/index.php/amc/article/view/2568
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FERI - Faculty of Electrical Engineering and Computer Science
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| 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 ▫$Q_d$▫ differ by at most one for every integer ▫$d$▫. In particular, if ▫$d$▫ is odd, then the metric and the edge metric dimensions of ▫$Q_d$▫ are equal. Second, we prove that the metric and the mixed metric dimensions of the hypercube ▫$Q_d$▫ are equal for every ▫$d \ge 3$▫. We conclude the paper by conjecturing that all these three types of metric dimensions of ▫$Q_d$▫ are equal when d is large enough. |
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| Keywords: | edge metric dimension, mixed metric dimension, metric dimension, hypercubes |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Submitted for review: | 24.02.2021 |
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| Article acceptance date: | 25.07.2022 |
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| Publication date: | 02.12.2022 |
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| Publisher: | Društvo matematikov, fizikov in astronomov, Društvo matematikov, fizikov in astronomov, Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije |
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| Year of publishing: | 2023 |
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| Number of pages: | art. P2.08 (9 str.) |
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| Numbering: | Vol. 23, no. 2 |
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| PID: | 20.500.12556/DKUM-88710  |
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| UDC: | 519.17 |
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| ISSN on article: | 1855-3966 |
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| COBISS.SI-ID: | 140460291 |
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| DOI: | 10.26493/1855-3974.2568.55c |
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| Publication date in DKUM: | 21.05.2024 |
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| Views: | 306 |
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| Downloads: | 20 |
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| Metadata: |    |
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| Categories: | Misc.
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