{"paper":{"title":"On the Strong Roman Domination Number of Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"I. Gonzalez Yero, J. C. Valenzuela, M. P. Alvarez-Ruiz, S. M. Sheikholeslami, T. Mediavilla-Gradolph","submitted_at":"2015-02-13T10:14:29Z","abstract_excerpt":"Based on the history that the Emperor Constantine decreed that any undefended place (with no legions) of the Roman Empire must be protected by a \"stronger\" neighbor place (having two legions), a graph theoretical model called Roman domination in graphs was described. A Roman dominating function for a graph $G=(V,E)$, is a function $f:V\\rightarrow \\{0,1,2\\}$ such that every vertex $v$ with $f(v)=0$ has at least a neighbor $w$ in $G$ for which $f(w)=2$. The Roman domination number of a graph is the minimum weight, $\\sum_{v\\in V}f(v)$, of a Roman dominating function.\n  In this paper we initiate t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.03933","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}