{"paper":{"title":"(Independent) Roman Domination Parameterized by Distance to Cluster","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.DS","math.CO"],"primary_cat":"cs.CC","authors_text":"Arti Pandey, Gautam K. Das, Kaustav Paul, Pradeesha Ashok, Subhabrata Paul","submitted_at":"2024-11-20T09:14:03Z","abstract_excerpt":"Given a graph $G=(V,E)$, a function $f:V\\to \\{0,1,2\\}$ is said to be a \\emph{Roman Dominating function} (RDF) if for every $v\\in V$ with $f(v)=0$, there exists a vertex $u\\in N(v)$ such that $f(u)=2$. A Roman Dominating function $f$ is said to be an \\emph{Independent Roman Dominating function} (IRDF), if $V_1\\cup V_2$ forms an independent set, where $V_i=\\{v\\in V~\\vert~f(v)=i\\}$, for $i\\in \\{0,1,2\\}$. The total weight of $f$ is equal to $\\sum_{v\\in V} f(v)$, and is denoted as $w(f)$. The \\emph{Roman Domination Number} (resp. \\emph{Independent Roman Domination Number}) of $G$, denoted by $\\gamm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.13141","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/2411.13141/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"}