{"paper":{"title":"On the Broadcast Independence Number of Locally Uniform 2-Lobsters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Eric Sopena (LaBRI), Isma Bouchemakh (L'IFORCE), Messaouda Ahmane (L'IFORCE)","submitted_at":"2019-02-08T10:04:34Z","abstract_excerpt":"Let $G$ be a simple undirected graph.A broadcast on $G$ isa function $f : V(G) \\to \\mathbf{N}$ such that $f(v)\\le e_G(v)$ holds for every vertex $v$ of $G$, where $e_G(v)$ denotes the eccentricity of $v$ in $G$, that is, the maximum distance from $v$ to any other vertex of $G$.The cost of $f$ is the value cost$(f)=\\sum_{v\\in V(G)}f(v)$.A broadcast $f$ on $G$ is independent if for every two distinct vertices $u$ and $v$ in $G$, $d_G(u,v)>\\max\\{f(u),f(v)\\}$,where $d_G(u,v)$ denotes the distance between $u$ and $v$ in $G$.The broadcast independence number of $G$ is then defined as the maximum cos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.02998","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"}