{"paper":{"title":"The $k$-metric dimension of the lexicographic product of graphs","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. Rodr\\'iguez-Vel\\'azquez","submitted_at":"2014-10-27T16:05:26Z","abstract_excerpt":"Given a simple and connected graph $G=(V,E)$, and a positive integer $k$, a set $S\\subseteq V$ is said to be a $k$-metric generator for $G$, if for any pair of different vertices $u,v\\in V$, there exist at least $k$ vertices $w_1,w_2,\\ldots,w_k\\in S$ such that $d_G(u,w_i)\\ne d_G(v,w_i)$, for every $i\\in \\{1,\\ldots,k\\}$, where $d_G(x,y)$ denotes the distance between $x$ and $y$. The minimum cardinality of a $k$-metric generator is the $k$-metric dimension of $G$. A set $S\\subseteq V$ is a $k$-adjacency generator for $G$ if any two different vertices $x,y\\in V(G)$ satisfy $|((N_G(x)\\triangledown"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7287","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"}