{"paper":{"title":"Bounds on metric dimension for families of planar graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carl Joshua Quines, Michael Sun","submitted_at":"2017-04-13T10:54:27Z","abstract_excerpt":"The concept of metric dimension has applications in a variety of fields, such as chemistry, robotic navigation, and combinatorial optimization. We show bounds for graphs with $n$ vertices and metric dimension $\\beta$. For Hamiltonian outerplanar graphs, we have $\\beta \\leq \\left\\lceil\\frac{n}2\\right\\rceil$; for outerplanar graphs in general, we have $\\beta \\leq \\left\\lfloor\\frac{2n}{3}\\right\\rfloor$; for maximal planar graphs, we have $\\beta \\leq \\left\\lfloor\\frac{3n}{4}\\right\\rfloor$. We also show that bipyramids have a metric dimension of $\\left\\lfloor\\frac{2n}{5}\\right\\rfloor + 1$. It is co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.04066","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"}