{"paper":{"title":"On the total and strong version for Roman dominating functions in graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"I.G. Yero, M. Soroudi, S.M. Sheikholeslami, S. Nazari-Moghaddam","submitted_at":"2019-12-02T21:55:35Z","abstract_excerpt":"Consider a finite and simple graph $G=(V,E)$ with maximum degree $\\Delta$. A strong Roman dominating function over the graph $G$ is understood as a map $f : V (G)\\rightarrow \\{0, 1,\\ldots , \\left\\lceil \\frac{\\Delta}{2}\\right\\rceil+ 1\\}$ which carries out the condition stating that all the vertices $v$ labeled $f(v)=0$ are adjacent to at least one another vertex $u$ that satisfies $f(u)\\geq 1+ \\left\\lceil \\frac{1}{2}\\vert N(u)\\cap V_0\\vert \\right\\rceil$, such that $V_0=\\{v \\in V \\mid f(v)=0 \\}$ and the notation $N(u)$ stands for the open neighborhood of $u$. The total version of one strong Roma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.01093","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/1912.01093/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"}