On metric dimensions of hypercubes

Kelenc, Aleksander (author), Masa Toshi, Aoden Teo (author), Škrekovski, Riste (author), Yero, Ismael G. (author)

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.

• Language: English
• Keywords: edge metric dimension, mixed metric dimension, metric dimension, hypercubes
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Publication date: 01.01.2023
• Year: 2023
• Number of pages: art. P2.08 (9 str.)
• Numbering: Vol. 23, no. 2
• PID: 20.500.12556/RUL-155087
• UDC: 519.17
• ISSN on article: 1855-3966
• DOI: 10.26493/1855-3974.2568.55c
• COBISS.SI-ID: 140460291
• Publication date in RUL: 19.03.2024

Record is a part of a journal

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

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