{"paper":{"title":"Total domination in cubic Kn\\\"odel graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Doost Ali Mojdeh, Esmaeil Nazari, Nader Jafari Rad, Seyed Reza Musawi","submitted_at":"2018-04-07T09:11:24Z","abstract_excerpt":"A subset $D$ of vertices of a graph $G$ is a \\textit{dominating set} if for each $u\\in V(G)\\setminus D$, $u$ is adjacent to some vertex $v\\in D$. The \\textit{dominating number}, $\\gamma(G)$ of $G$, is the minimum cardinality of a dominating set of $G$. A set $D\\subseteq V(G)$ is a \\textit{total dominating set} if for each $u\\in V(G)$, $u$ is adjacent to some vertex $v\\in D$. the The \\textit{total dominating number}, $\\gamma_t(G)$ of $G$, is the minimum cardinality of a total dominating set of $G$. For an even integer $n\\ge2$ and $1\\le\\Delta\\le\\lfloor\\log_2n\\rfloor$, a \\textit{Kn\\\"odel graph} $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.02532","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"}