{"paper":{"title":"Convex and weakly convex domination in prism graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Monika Rosicka","submitted_at":"2017-12-20T15:56:11Z","abstract_excerpt":"For a given graph $G=(V,E)$ and permutation $\\pi:V\\mapsto V$ the prism $\\pi G$ of $G$ is defined as follows: $V(\\pi G)=V(G)\\cup V(G')$, where $G'$ is a copy of $G$, and $E(\\pi G)=E(G)\\cup E(G')\\cup M_{\\pi}$, where $M_{\\pi}=\\{uv': u\\in V(G), v=\\pi(u)\\}$ and $v'$ denotes the copy of $v$ in $G'$.\n  We study and compare the properties of convex and weakly convex dominating sets in prism graphs. In particular, we characterize prism $\\gamma_{con}$-fixers and -doublers. We also show that the differences $\\gamma_{wcon}(G)-\\gamma_{wcon}(\\pi G)$ and $\\gamma_{wcon}(\\pi G) - 2\\gamma_{wcon}(G)$ can be arbi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.07545","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"}