{"paper":{"title":"Multiset Metric Dimension of Binomial Random Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Austin Eide, Pawel Pralat","submitted_at":"2025-07-15T19:41:23Z","abstract_excerpt":"For a graph $G = (V,E)$ and a subset $R \\subseteq V$, we say that $R$ is \\textit{multiset resolving} for $G$ if for every pair of vertices $v,w$, the \\textit{multisets} $\\{d(v,r): r \\in R\\}$ and $\\{d(w,r):r \\in R\\}$ are distinct, where $d(x,y)$ is the graph distance between vertices $x$ and $y$. The \\textit{multiset metric dimension} of $G$ is the size of a smallest set $R \\subseteq V$ that is multiset resolving (or $\\infty$ if no such set exists). This graph parameter was introduced by Simanjuntak, Siagian, and Vitr\\'{i}k in 2017~\\cite{simanjuntak2017multiset}, and has since been studied for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.11686","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.11686/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}