{"paper":{"title":"Domination in Functigraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Cong X. Kang, Craig E. Larson, Eunjeong Yi, Linda Eroh, Ralucca Gera","submitted_at":"2011-06-06T18:52:32Z","abstract_excerpt":"Let $G_1$ and $G_2$ be disjoint copies of a graph $G$, and let $f: V(G_1) \\rightarrow V(G_2)$ be a function. Then a \\emph{functigraph} $C(G, f)=(V, E)$ has the vertex set $V=V(G_1) \\cup V(G_2)$ and the edge set $E=E(G_1) \\cup E(G_2) \\cup \\{uv \\mid u \\in V(G_1), v \\in V(G_2), v=f(u)\\}$. A functigraph is a generalization of a \\emph{permutation graph} (also known as a \\emph{generalized prism}) in the sense of Chartrand and Harary. In this paper, we study domination in functigraphs. Let $\\gamma(G)$ denote the domination number of $G$. It is readily seen that $\\gamma(G) \\le \\gamma(C(G,f)) \\le 2 \\ga"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1147","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"}