{"paper":{"title":"On the weak $k$-metric dimension of Hamming graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dorota Kuziak, Elena Fernandez, Ismael G. Yero, Manuel Mu\\~noz-Marquez, Sandi Klavzar","submitted_at":"2025-05-26T07:59:45Z","abstract_excerpt":"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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.19642","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.19642/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}