{"paper":{"title":"The Simultaneous Strong Metric Dimension of Graph Families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A. Estrada-Moreno, C. Garc\\'ia-G\\'omez, J. A. Rodr\\'iguez-Vel\\'azquez, Y. Ram\\'irez-Cruz","submitted_at":"2015-04-19T11:01:37Z","abstract_excerpt":"Let ${\\cal G}$ be a family of graphs defined on a common (labeled) vertex set $V$. A set $S\\subset V$ is said to be a simultaneous strong metric generator for ${\\cal G}$ if it is a strong metric generator for every graph of the family. The minimum cardinality among all simultaneous strong metric generators for ${\\cal G}$, denoted by $Sd_s({\\cal G})$, is called the simultaneous strong metric dimension of ${\\cal G}$. We obtain general results on $Sd_s({\\cal G})$ for arbitrary families of graphs, with special emphasis on the case of families composed by a graph and its complement. In particular, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04820","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"}