20.500.12556/DiRROS-18477 On metric dimensions of hypercubes 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. edge metric dimension mixed metric dimension metric dimension hypercubes metrična dimenzija roba mešana metrična dimenzija metrična dimenzija hiperkocke true false true Angleški jezik Slovenski jezik Neznano 2024-03-19 13:23:25 2024-03-19 13:23:25 2024-03-20 03:39:24 0000-00-00 00:00:00 2023 0 0 art. P2.08 (9 str.) no. 2 Vol. 23 2023 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2023-01-01 519.17 1855-3966 10.26493/1855-3974.2568.55c 140460291 amc_2568-1.pdf amc_2568-1.pdf 1 471024FA77393163F7146F394B03EFFA bcb14787afb9e74e4b27afcb111ddf4fd4543061d351a37b825db48da1192a2b b3928f6f-e5eb-11ee-9dd4-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=25172 Inštitut za matematiko, fiziko in mehaniko 0 0 0