{"paper":{"title":"The k-metric dimension of graphs: a general approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A. Estrada-Moreno, I. G. Yero, J. A. Rodriguez-Velazquez","submitted_at":"2016-05-21T23:44:41Z","abstract_excerpt":"Let $(X,d)$ be a metric space. A set $S\\subseteq X$ is said to be a $k$-metric generator for $X$ if and only if for any pair of different points $u,v\\in X$, there exist at least $k$ points $w_1,w_2, \\ldots w_k\\in S$ such that $d(u,w_i)\\ne d(v,w_i),\\; \\mbox{\\rm for all}\\; i\\in \\{1, \\ldots k\\}.$ Let $\\mathcal{R}_k(X)$ be the set of metric generators for $X$. The $k$-metric dimension $\\dim_k(X)$ of $(X,d)$ is defined as $$\\dim_k(X)=\\inf\\{|S|:\\, S\\in \\mathcal{R}_k(X)\\}.$$ Here, we discuss the $k$-metric dimension of $(V,d_t)$, where $V$ is the set of vertices of a simple graph $G$ and the metric $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06709","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}