{"paper":{"title":"Identifying codes in line graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Aline Parreau (IF), Florent Foucaud (LaBRI), Petru Valicov (LaBRI), Reza Naserasr (LaBRI), Sylvain Gravier (IF)","submitted_at":"2011-07-01T12:18:42Z","abstract_excerpt":"An identifying code of a graph is a subset of its vertices such that every vertex of the graph is uniquely identified by the set of its neighbours within the code. We study the edge-identifying code problem, i.e. the identifying code problem in line graphs. If $\\ID(G)$ denotes the size of a minimum identifying code of an identifiable graph $G$, we show that the usual bound $\\ID(G)\\ge \\lceil\\log_2(n+1)\\rceil$, where $n$ denotes the order of $G$, can be improved to $\\Theta(\\sqrt{n})$ in the class of line graphs. Moreover, this bound is tight. We also prove that the upper bound $\\ID(\\mathcal{L}(G"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0207","kind":"arxiv","version":2},"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"}