{"paper":{"title":"Critical properties on Roman domination graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A. Mart\\'inez-P\\'erez, D. Oliveros","submitted_at":"2013-11-18T18:14:32Z","abstract_excerpt":"A Roman domination function on a graph G is a function $r:V(G)\\to \\{0,1,2\\}$ satisfying the condition that every vertex $u$ for which $r(u)=0$ is adjacent to at least one vertex $v$ for which $r(v)=2$. The weight of a Roman function is the value $r(V(G))=\\sum_{u\\in V(G)}r(u)$. The Roman domination number $\\gamma_R(G)$ of $G$ is the minimum weight of a Roman domination function on $G$. \"Roman Criticality\" has been defined in general as the study of graphs where the Roman domination number decreases when removing an edge or a vertex of the graph. In this paper we give further results in this top"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4476","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"}