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The Roman domination number $\\gamma_{\\rm R}(G)$ is defined as the minimum weight of all Roman dominating functions. This paper defines the Roman bondage number $b_{\\rm R}(G)$ of a nonempty graph $G=(V,E)$ to be the cardinality among all sets of edges $B\\subseteq E$ for which $\\gamma_{\\rm R}(G-B)>\\gamma_{\\rm R}(G)$. Some bounds are obtain"},"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":"1109.3930","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-09-19T02:54:33Z","cross_cats_sorted":[],"title_canon_sha256":"2ff0709c3c9ea73e46f402d97e7f0d8daa1c37fd3a0af437ad52486a8780ea9d","abstract_canon_sha256":"f74d159bdc97ec82c4c175229df90e8de4bc1eccf86bd4b7a76329ec44578d04"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:45.557948Z","signature_b64":"IkRc7DXfgxVTHNcZ6eAno8rkBMbhZ6mE/UosD4xxlDHJEfuCQ9XW6jUY9HK8IF0TKpgfkFUZQtllhNglmw8tDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e796235d19d66e6c22765a77a16c98375a07a5e2c29d7caf53261890d86fecb7","last_reissued_at":"2026-05-18T04:12:45.557480Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:45.557480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Roman Bondage Number of a Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Fu-Tao Hu, Jun-Ming Xu","submitted_at":"2011-09-19T02:54:33Z","abstract_excerpt":"The Roman dominating function on a graph $G=(V,E)$ is a function $f: V\\rightarrow\\{0,1,2\\}$ such that each vertex $x$ with $f(x)=0$ is adjacent to at least one vertex $y$ with $f(y)=2$. The value $f(G)=\\sum\\limits_{u\\in V(G)} f(u)$ is called the weight of $f$. The Roman domination number $\\gamma_{\\rm R}(G)$ is defined as the minimum weight of all Roman dominating functions. This paper defines the Roman bondage number $b_{\\rm R}(G)$ of a nonempty graph $G=(V,E)$ to be the cardinality among all sets of edges $B\\subseteq E$ for which $\\gamma_{\\rm R}(G-B)>\\gamma_{\\rm R}(G)$. 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