{"paper":{"title":"Outer independent double Roman domination number of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Babak Samadi, Doost Ali Mojdeh, Ismael G. Yero, Zehui Shao","submitted_at":"2019-08-20T13:17:15Z","abstract_excerpt":"A double Roman dominating function of a graph $G$ is a function $f:V(G)\\rightarrow \\{0,1,2,3\\}$ having the property that for each vertex $v$ with $f(v)=0$, there exists $u\\in N(v)$ with $f(u)=3$, or there are $u,w\\in N(v)$ with $f(u)=f(w)=2$, and if $f(v)=1$, then $v$ is adjacent to a vertex assigned at least $2$ under $f$. The double Roman domination number $\\gamma_{dR}(G)$ is the minimum weight $f(V(G))=\\sum_{v\\in V(G)}f(v)$ among all double Roman dominating functions of $G$. An outer independent double Roman dominating function is a double Roman dominating function $f$ for which the set of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.01775","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1909.01775/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}