20.500.12556/DiRROS-28314 On the weak $k$-metric dimension of Hamming graphs Given a connected graph $G$, a set of vertices $X\subset V(G)$ is a weak $k$-resolving set of $G$ if for each two vertices $y,z\in V(G)$, the sum of the values $|d_G(y,x)-d_G(z,x)|$ over all $x\in X$ is at least $k$, where $d_G(u,v)$ stands for the length of a shortest path between $u$ and $v$. The cardinality of a smallest weak $k$-resolving set of $G$ is the weak $k$-metric dimension of $G$, and is denoted by $\mathrm{wdim}_k(G)$. In this paper, $\mathrm{wdim}_k(K_n\,\square\,K_n)$ is determined for every $n\ge 3$ and every $2\le k\le 2n$. An improvement of a known integer linear programming formulation for this problem is developed and implemented for the graphs $K_n\,\square\,K_m$. Conjectures regarding these general situations are posed. weak $k$-metric dimension weak $k$-resolving set Cartesian product Hamming graph šibka $k$-metrična dimenzija šibka $k$-solventna množica kartezični produkt Hammingov graf true false true Angleški jezik Slovenski jezik Neznano 2026-03-13 13:40:44 2026-03-13 13:40:44 2026-03-14 04:26:01 0000-00-00 00:00:00 2026 0 0 12 str. article no. 100945 Vol. 60 May 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2026-05-01 519.17:519.8 1572-5286 10.1016/j.disopt.2026.100945 271637763 1-s2.0-S1572528626000186-main.pdf 1-s2.0-S1572528626000186-main.pdf 1 B763044489102E3BF1A567EDEFD8DE93 1b7bc618eea30944ba372f294ac06c14bbc26ece78d7b4783d06a6b5ae1bc9b1 cc2bed1f-1eda-11f1-acf8-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=41814 https://www.sciencedirect.com/science/article/pii/S1572528626000186 1 dcbe1838-1ed9-11f1-acf8-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=41809 Inštitut za matematiko, fiziko in mehaniko 0 0 0