{"paper":{"title":"Domination in designs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Deepak Rajendraprasad, Felix Goldberg, Rogers Mathew","submitted_at":"2014-05-14T10:19:18Z","abstract_excerpt":"We commence the study of domination in the incidence graphs of combinatorial designs. Let $D$ be a combinatorial design and denote by $\\gamma(D)$ the domination number of the incidence (Levy) graph of $D$. We obtain a number of results about the domination numbers of various kinds of designs.\n  For instance, a finite projective plane of order $n$, which is a symmetric $(n^{2}+n+1,n+1,1)$-design, has $\\gamma=2n$. %We also show that for any symmetric $(v,k,\\lambda)$-design it holds that $\\gamma \\leq 2k$. We study at depth the domination numbers of Steiner systems and in particular of Steiner tri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.3436","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"}