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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1106.1147","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-06-06T18:52:32Z","cross_cats_sorted":[],"title_canon_sha256":"4a9a193ad06f2bf3d3df28a66676342e17d3b35d07f56372ce7a5b35777c6cc4","abstract_canon_sha256":"d36c7f63ad2b2d48ad0f6fc671e7ffc281495d6fe2a048554ee56afc6928e637"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:53.462868Z","signature_b64":"cWhvz5CciMkP8aQD6nZDICQVi0U12ISP/1jZ50bYcoaWljL/0v8f6keXFbYpDcS1H21G/P2vYisYMPOFRpc9Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d7a471d1979f7e70b39e9924131c3a651b87d4567a10d699de16331a8b458c1","last_reissued_at":"2026-05-18T03:57:53.462236Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:53.462236Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $G$. 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