{"paper":{"title":"The Domination Number of Generalized Petersen Graphs with a Faulty Vertex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Jun-Lin Guo, Kuo-Hua Wu, Ton Kloks, Yue-Li Wang","submitted_at":"2013-05-07T00:47:55Z","abstract_excerpt":"In this paper, we investigate the domination number of generalized Petersen graphs P(n, 2) when there is a faulty vertex. Denote by $\\gamma(P(n,2))$ the domination number of P(n,2) and $\\gamma(P_f(n,2))$ the domination number of P(n,2) with a faulty vertex $u_f$. We show that $\\gamma(P_f(n,2))=\\gamma(P(n,2))-1$ when $n=5k+1$ or $5k+2$ and $\\gamma(P_f(n,2))=\\gamma(P(n,2))$ for the other cases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1366","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"}