{"paper":{"title":"Uniquely dimensional graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Behnaz Omoomi, Behrooz Bagheri, Mohsen Jannesari","submitted_at":"2012-05-02T06:01:11Z","abstract_excerpt":"A set $W\\subseteq V(G)$ is called a resolving set, if for each two distinct vertices $u,v\\in V(G)$ there exists $w\\in W$ such that $d(u,w)\\neq d(v,w)$, where $d(x,y)$ is the distance between the vertices $x$ and $y$. A resolving set for $G$ with minimum cardinality is called a metric basis.\n  A graph with a unique metric basis is called a uniquely dimensional graph.\n  In this paper, we study some properties of uniquely dimensional graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0327","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"}