{"paper":{"title":"On weak metric dimension of digraphs","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Kaishun Wang, Min Feng, Yuefeng Yang","submitted_at":"2020-11-24T11:31:21Z","abstract_excerpt":"Using the two way distance, we introduce the concepts of weak metric dimension of a strongly connected digraph $\\Gamma$. We first establish lower and upper bounds for the number of arcs in $\\Gamma$ by using the diameter and weak metric dimension of $\\Gamma$, and characterize all digraphs attaining the lower or upper bound. Then we study a digraph with weak metric dimension $1$ and classify all vertex-transitive digraphs having weak metric dimension $1$. Finally, all digraphs of order $n$ with weak metric dimension $n-1$ or $n-2$ are determined."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.12038","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2011.12038/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"}