{"paper":{"title":"On the Domination Number of Generalized Petersen Graphs P(ck,k)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guoqing Wang, Haoli Wang, Xirong Xu, Yuansheng Yang","submitted_at":"2011-03-12T07:22:33Z","abstract_excerpt":"Let $G=(V(G),E(G))$ be a simple connected and undirected graph with vertex set $V(G)$ and edge set $E(G)$. A set $S \\subseteq V(G)$ is a $dominating$ $set$ if for each $v \\in V(G)$ either $v \\in S$ or $v$ is adjacent to some $w \\in S$. That is, $S$ is a dominating set if and only if $N[S]=V(G)$. The domination number $\\gamma(G)$ is the minimum cardinalities of minimal dominating sets. In this paper, we give an improved upper bound on the domination number of generalized Petersen graphs $P(ck,k)$ for $c\\geq 3$ and $k\\geq 3$. We also prove that $\\gamma(P(4k,k))=2k+1$ for even $k$, $\\gamma(P(5k,k"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2427","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"}