{"paper":{"title":"Small domination-type invariants in random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Michitaka Furuya, Tamae Kawasaki","submitted_at":"2019-06-27T15:44:31Z","abstract_excerpt":"For $c\\in \\mathbb{R}^{+}\\cup \\{\\infty \\}$ and a graph $G$, a function $f:V(G)\\rightarrow \\{0,1,c\\}$ is called a $c$-self dominating function of $G$ if for every vertex $u\\in V(G)$, $f(u)\\geq c$ or $\\max\\{f(v):v\\in N_{G}(u)\\}\\geq 1$ where $N_{G}(u)$ is the neighborhood of $u$ in $G$. The minimum weight $w(f)=\\sum _{u\\in V(G)}f(u)$ of a $c$-self dominating function $f$ of $G$ is called the $c$-self domination number of $G$. The $c$-self domination concept is a common generalization of three domination-type invariants; (original) domination, total domination and Roman domination. In this paper, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.11743","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":""},"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"}