{"paper":{"title":"Edge metric dimension of some graph operations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ismael G. Yero, Iztok Peterin","submitted_at":"2018-09-24T13:18:13Z","abstract_excerpt":"Let $G=(V, E)$ be a connected graph. Given a vertex $v\\in V$ and an edge $e=uw\\in E$, the distance between $v$ and $e$ is defined as $d_G(e,v)=\\min\\{d_G(u,v),d_G(w,v)\\}$. A nonempty set $S\\subset V$ is an edge metric generator for $G$ if for any two edges $e_1,e_2\\in E$ there is a vertex $w\\in S$ such that $d_G(w,e_1)\\ne d_G(w,e_2)$. The minimum cardinality of any edge metric generator for a graph $G$ is the edge metric dimension of $G$. The edge metric dimension of the join, lexicographic and corona product of graphs is studied in this article."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08900","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"}