| 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: |  PDF - Presentation file, download (259,98 KB)
MD5: 471024FA77393163F7146F394B03EFFA
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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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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| Publication date: | 01.01.2023 |
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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/DiRROS-18477  |
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| UDC: | 519.17 |
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| ISSN on article: | 1855-3966 |
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| DOI: | 10.26493/1855-3974.2568.55c |
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| COBISS.SI-ID: | 140460291 |
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| Note: |
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| Publication date in DiRROS: | 19.03.2024 |
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| Views: | 145 |
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| Downloads: | 40 |
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| Metadata: |     |
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