{"paper":{"title":"Total Roman 2-domination in graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Abel Cabrera Martinez, Frank A. Hernandez Mira, Ismael G. Yero, Suitberto Cabrera Garcia","submitted_at":"2021-01-07T13:48:03Z","abstract_excerpt":"Given a graph $G=(V,E)$, a function $f:V\\rightarrow \\{0,1,2\\}$ is a total Roman $\\{2\\}$-dominating function if: (1) every vertex $v\\in V$ for which $f(v)=0$ satisfies that $\\sum_{u\\in N(v)}f(u)\\geq 2$, where $N(v)$ represents the open neighborhood of $v$, and (2) every vertex $x\\in V$ for which $f(x)\\geq 1$ is adjacent to at least one vertex $y\\in V$ such that $f(y)\\geq 1$. The weight of the function $f$ is defined as $\\omega(f)=\\sum_{v\\in V}f(v)$. The total Roman $\\{2\\}$-domination number, denoted by $\\gamma_{t\\{R2\\}}(G)$, is the minimum weight among all total Roman $\\{2\\}$-dominating functio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.02537","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/2101.02537/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"}