{"paper":{"title":"On The Double Roman bondage numbers of Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"F. Rahimi Mahid, H.R. Maimani, M. Momeni, N. Jafari Rad","submitted_at":"2019-05-16T13:17:12Z","abstract_excerpt":"For a graph $G=(V,E)$, a double roman dominating function (DRDF) is a function $f : V \\longrightarrow \\{0, 1, 2,3\\}$ having the property that if $f(v)=0$ for some vertex $v$, then $v$ has at least two neighbors assigned $2$ under $f$ or one neighbor $w$ with $f(w)=3$, and if $f(v)=1$ then $v$ has at least one neighbor $w$ with $f(w) \\geq 2$. The weight of a DRDF $f$ is the sum $f (V) =\\sum_{u\\in V} f (u)$. The minimum weight of a DRDF on a graph $G$ is the double Roman domination number of $G$ and is denoted by $\\gamma_{dR}(G)$. The double roman bondage number of $G$, denoted by $b_{dR}(G)$, i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.06724","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"}