{"paper":{"title":"Signed Total Roman Domination and Domatic Numbers: Degree Three and Complete Multipartite Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Arie M. C. A. Koster, Lutz Volkmann, Moritz Wehrmann","submitted_at":"2026-06-25T15:41:54Z","abstract_excerpt":"Signed total Roman domination is a variant of the classic Roman domination-problem in graphs. A signed total Roman dominating function (STRD function) on a graph $G=(V,E)$ is a function $f: V \\to \\{-1,1,2\\}$ such that (i) $\\sum_{u \\in N(v)} f(u) \\geq 1$ for all $v \\in V$, where $N(v)$ denotes the neighborhood of $v$, and (ii) every vertex $v$ with $f(v) = -1$ is adjacent to a vertex $u$ with $f(u) = 2$. The weight of $f$ is $\\sum_{v \\in V} f(v)$. The signed total Roman domination number of $G$ is the minimum weight among all its STRD functions. A signed total Roman dominating family (STRD fami"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27175","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/2606.27175/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"}