{"paper":{"title":"On the integer {k}-domination number of circulant graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Chia-an Liu, Hung-Lin Fu, Yen-Jen Cheng","submitted_at":"2019-05-08T23:14:56Z","abstract_excerpt":"Let $G=(V,E)$ be a simple undirected graph. $G$ is a circulant graph defined on $V=\\mathbb{Z}_n$ with difference set $D\\subseteq \\{1,2,\\ldots,\\lfloor\\frac{n}{2}\\rfloor\\}$ provided two vertices $i$ and $j$ in $\\mathbb{Z}_n$ are adjacent if and only if $\\min\\{|i-j|, n-|i-j|\\}\\in D$. For convenience, we use $G(n;D)$ to denote such a circulant graph.\n  A function $f:V(G)\\rightarrow\\mathbb{N}\\cup\\{0\\}$ is an integer $\\{k\\}$-domination function if for each $v\\in V(G)$, $\\sum_{u\\in N_G[v]}f(u)\\geq k.$ By considering all $\\{k\\}$-domination functions $f$, the minimum value of $\\sum_{v\\in V(G)}f(v)$ is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.03388","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"}