{"paper":{"title":"A Note on Roman \\{2\\}-domination problem in graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.CO","authors_text":"Changhong Lu, Hangdi Chen","submitted_at":"2018-04-25T04:10:45Z","abstract_excerpt":"For a graph $G=(V,E)$, a Roman $\\{2\\}$-dominating function (R2DF)$f:V\\rightarrow \\{0,1,2\\}$ has the property that for every vertex $v\\in V$ with $f(v)=0$, either there exists a neighbor $u\\in N(v)$, with $f(u)=2$, or at least two neighbors $x,y\\in N(v)$ having $f(x)=f(y)=1$. The weight of a R2DF is the sum $f(V)=\\sum_{v\\in V}{f(v)}$, and the minimum weight of a R2DF is the Roman $\\{2\\}$-domination number $\\gamma_{\\{R2\\}}(G)$. A R2DF is independent if the set of vertices having positive function values is an independent set. The independent Roman $\\{2\\}$-domination number $i_{\\{R2\\}}(G)$ is the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09338","kind":"arxiv","version":3},"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"}