{"paper":{"title":"Roman Bondage Number of a Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Fu-Tao Hu, Jun-Ming Xu","submitted_at":"2011-09-19T02:54:33Z","abstract_excerpt":"The Roman dominating function on a graph $G=(V,E)$ is a function $f: V\\rightarrow\\{0,1,2\\}$ such that each vertex $x$ with $f(x)=0$ is adjacent to at least one vertex $y$ with $f(y)=2$. The value $f(G)=\\sum\\limits_{u\\in V(G)} f(u)$ is called the weight of $f$. The Roman domination number $\\gamma_{\\rm R}(G)$ is defined as the minimum weight of all Roman dominating functions. This paper defines the Roman bondage number $b_{\\rm R}(G)$ of a nonempty graph $G=(V,E)$ to be the cardinality among all sets of edges $B\\subseteq E$ for which $\\gamma_{\\rm R}(G-B)>\\gamma_{\\rm R}(G)$. Some bounds are obtain"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.3930","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"}