{"paper":{"title":"The Simultaneous Metric Dimension of Families Composed by Lexicographic Product Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alejandro Estrada-Moreno, Juan A. Rodriguez-Velazquez, Yunior Ramirez-Cruz","submitted_at":"2015-04-02T09:43:31Z","abstract_excerpt":"Let ${\\mathcal G}$ be a graph family defined on a common (labeled) vertex set $V$. A set $S\\subseteq V$ is said to be a simultaneous metric generator for ${\\cal G}$ if for every $G\\in {\\cal G}$ and every pair of different vertices $u,v\\in V$ there exists $s\\in S$ such that $d_{G}(s,u)\\ne d_{G}(s,v)$, where $d_{G}$ denotes the geodesic distance. A simultaneous adjacency generator for ${\\cal G}$ is a simultaneous metric generator under the metric $d_{G,2}(x,y)=\\min\\{d_{G}(x,y),2\\}$. A minimum cardinality simultaneous metric (adjacency) generator for ${\\cal G}$ is a simultaneous metric (adjacency"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00492","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":""},"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"}