{"paper":{"title":"Roman domination number of Generalized Petersen Graphs P(n,2)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Chunnian Ji, Haoli Wang, Xirong Xu, Yuansheng Yang","submitted_at":"2011-03-12T03:56:44Z","abstract_excerpt":"A $Roman\\ domination\\ function$ on a graph $G=(V, E)$ is a function $f:V(G)\\rightarrow\\{0,1,2\\}$ satisfying the condition that every vertex $u$ with $f(u)=0$ is adjacent to at least one vertex $v$ with $f(v)=2$. The $weight$ of a Roman domination function $f$ is the value $f(V(G))=\\sum_{u\\in V(G)}f(u)$. The minimum weight of a Roman dominating function on a graph $G$ is called the $Roman\\ domination\\ number$ of $G$, denoted by $\\gamma_{R}(G)$. In this paper, we study the {\\it Roman domination number} of generalized Petersen graphs P(n,2) and prove that $\\gamma_R(P(n,2)) = \\lceil {\\frac{8n}{7}}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2419","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"}