On metric dimensions of hypercubes
Aleksander Kelenc, Aoden Teo Masa Toshi, Riste Škrekovski, Ismael G. Yero · Ars Mathematica Contemporanea · 2022
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.