{"paper":{"title":"The Simultaneous Metric Dimension of Graph Families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"J. A. Rodriguez-Velazquez, O. R. Oellermann, Y. Ramirez-Cruz","submitted_at":"2015-01-03T13:40:43Z","abstract_excerpt":"A vertex $v\\in V$ is said to resolve two vertices $x$ and $y$ if $d_G(v,x)\\ne d_G(v,y)$. A set $S\\subset V$ is said to be a metric generator for $G$ if any pair of vertices of $G$ is resolved by some element of $S$. A minimum metric generator is called a metric basis, and its cardinality, $\\dim(G)$, the \\emph{metric dimension} of $G$. A set $S\\subseteq V$ is said to be a simultaneous metric generator for a graph family ${\\cal G}=\\{G_1,G_2,\\ldots,G_k\\}$, defined on a common (labeled) vertex set, if it is a metric generator for every graph of the family. A minimum cardinality simultaneous metric"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00565","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"}