On metric dimensions of hypercubes

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

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

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DOI: https://doi.org/10.26493/1855-3974.2568.55c

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications