{"paper":{"title":"Locating domination in bipartite graphs and their complements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carmen Hernando, Ignacio M. Pelayo, Merc\\`e Mora","submitted_at":"2017-11-03T10:07:52Z","abstract_excerpt":"A set $S$ of vertices of a graph $G$ is \\emph{distinguishing} if the sets of neighbors in $S$ for every pair of vertices not in $S$ are distinct. A \\emph{locating-dominating set} of $G$ is a dominating distinguishing set. The \\emph{location-domination number} of $G$, $\\lambda(G)$, is the minimum cardinality of a locating-dominating set. In this work we study relationships between $\\lambda({G})$ and $\\lambda (\\overline{G})$ for bipartite graphs. The main result is the characterization of all connected bipartite graphs $G$ satisfying $\\lambda (\\overline{G})=\\lambda({G})+1$. To this aim, we defin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.01951","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":""},"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"}