{"paper":{"title":"On Edge Dimension of a Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Nina Zubrilina","submitted_at":"2016-11-07T06:31:42Z","abstract_excerpt":"Given a connected graph $G(V, E)$, the edge dimension, denoted $\\mathrm{edim}(G)$, is the least size of a set $S \\subseteq V$ that distinguishes every pair of edges of $G$, in the sense that the edges have pairwise distinct tuples of distances to the vertices of $S$. The notation was introduced by Kelenc, Tratnik, and Yero, and in their paper, they asked several questions about properties of $\\mathrm{edim}$. In this article we answer two of these questions: we classify the graphs for which $\\mathrm{edim}(G) = n-1$ and show that $\\frac{\\mathrm{edim}(G)}{\\dim(G)}$ isn't bounded from above (here "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01904","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"}