{"paper":{"title":"On Metric Dimension of Functigraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Cong X. Kang, Eunjeong Yi, Linda Eroh","submitted_at":"2011-11-24T22:29:40Z","abstract_excerpt":"The \\emph{metric dimension} of a graph $G$, denoted by $\\dim(G)$, is the minimum number of vertices such that each vertex is uniquely determined by its distances to the chosen vertices. Let $G_1$ and $G_2$ be disjoint copies of a graph $G$ and let $f: V(G_1) \\rightarrow V(G_2)$ be a function. Then a \\emph{functigraph} $C(G, f)=(V, E)$ has the vertex set $V=V(G_1) \\cup V(G_2)$ and the edge set $E=E(G_1) \\cup E(G_2) \\cup \\{uv \\mid v=f(u)\\}$. We study how metric dimension behaves in passing from $G$ to $C(G,f)$ by first showing that $2 \\le \\dim(C(G, f)) \\le 2n-3$, if $G$ is a connected graph of o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5864","kind":"arxiv","version":3},"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"}