{"paper":{"title":"Roman domination excellent graphs: trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Vladimir Samodivkin","submitted_at":"2016-10-02T15:58:00Z","abstract_excerpt":"A Roman dominating function (RDF) on a graph $G = (V, E)$ is a labeling $f : V \\rightarrow \\{0, 1, 2\\}$ such that every vertex with label $0$ has a neighbor with label $2$. The weight of $f$ is the value $f(V) = \\Sigma_{v\\in V} f(v)$. The Roman domination number, $\\gamma_R(G)$, of $G$ is the minimum weight of an RDF on $G$. An RDF of minimum weight is called a $\\gamma_R$-function. A graph G is said to be $\\gamma_R$-excellent if for each vertex $x \\in V$ there is a $\\gamma_R$-function $h_x$ on $G$ with $h_x(x) \\not = 0$. We present a constructive characterization of $\\gamma_R$-excellent trees u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00297","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"}