{"paper":{"title":"On the super domination number of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Douglas J. Klein, Eunjeong Yi, Juan A. Rodr\\'iguez-Vel\\'azquez","submitted_at":"2017-05-02T12:01:31Z","abstract_excerpt":"The open neighbourhood of a vertex $v$ of a graph $G$ is the set $N(v)$ consisting of all vertices adjacent to $v$ in $G$. For $D\\subseteq V(G)$, we define $\\overline{D}=V(G)\\setminus D$. A set $D\\subseteq V(G)$ is called a super dominating set of $G$ if for every vertex $u\\in \\overline{D}$, there exists $v\\in D$ such that $N(v)\\cap \\overline{D}=\\{u\\}$. The super domination number of $G$ is the minimum cardinality among all super dominating sets in $G$. In this article, we obtain closed formulas and tight bounds for the super domination number of $G$ in terms of several invariants of $G$. Furt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00928","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"}