{"paper":{"title":"k-Metric Antidimension: a Privacy Measure for Social Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DB"],"primary_cat":"math.CO","authors_text":"Ismael G. Yero, Rolando Trujillo-Rasua","submitted_at":"2014-08-09T21:08:48Z","abstract_excerpt":"Let $G = (V, E)$ be a simple connected graph and $S = \\{w_1, \\cdots, w_t\\} \\subseteq V$ an ordered subset of vertices. The metric representation of a vertex $u\\in V$ with respect to $S$ is the $t$-vector $r(u|S) = (d_G(u, w_1), \\cdots, d_G(u, w_t))$, where $d_G(u, v)$ represents the length of a shortest $u-v$ path in $G$. The set $S$ is called a resolving set for $G$ if $r(u|S) = r(v|S)$ implies $u = v$ for every $u, v \\in V$. The smallest cardinality of a resolving set is the metric dimension of $G$. In this article we propose, to the best of our knowledge, a new problem in Graph Theory that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2154","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"}