{"paper":{"title":"On the Partition Dimension and the Twin Number of a Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carmen Hernando, Ignacio M Pelayo, Merce Mora","submitted_at":"2016-02-29T11:16:38Z","abstract_excerpt":"A partition P of the vertex set of a connected graph G is a locating partition of G if every vertex is uniquely determined by its vector of distances to the elements of P. The partition dimension of G is the minimum cardinality of a locating partition of G. A pair of vertices u,v of a graph G are called twins if they have exactly the same set of neighbors other than u and v. A twin class is a maximal set of pairwise twin vertices. The twin number of a graph G is the maximum cardinality of a twin class of G.\n  In this paper we undertake the study of the partition dimension of a graph by also co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.08907","kind":"arxiv","version":3},"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"}