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On metric dimensions of hypercubesAleksander Kelenc,
Aoden Teo Masa Toshi,
Riste Škrekovski,
Ismael G. Yero, 2023, original scientific article
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.
Keywords: edge metric dimension, mixed metric dimension, metric dimension, hypercubes
Published in DiRROS: 19.03.2024; Views: 133; Downloads: 36
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