{"paper":{"title":"On the Roman bondage number of a graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A. Bahremandpour, Fu-Tao Hu, Jun-Ming Xu, S. M. Sheikholeslami","submitted_at":"2012-04-06T09:02:19Z","abstract_excerpt":"A Roman dominating function on a graph $G=(V,E)$ is a function $f:V\\rightarrow\\{0,1,2\\}$ such that every vertex $v\\in V$ with $f(v)=0$ has at least one neighbor $u\\in V$ with $f(u)=2$. The weight of a Roman dominating function 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, denoted by $\\gamma_{R}(G)$. The Roman bondage number $b_{R}(G)$ of a graph $G$ with maximum degree at least two is the minimum cardinality of all sets $E'\\subseteq E(G)$ for which $\\gamma_{R}(G-E')>\\gamma_R(G)$. In this pape"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1438","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"}