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The Roman bondage number $b_R(G)$ is the cardinality of a smallest set of edges whose removal from $G$ results in a graph with Roman domination number not equal to $\\gamma_R(G)$. In this paper we obtain upper bounds on $b_{R}(G)$ in terms of (a) the average degree and maximum degree, and (b) Euler characteristic, girth a"},"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":"1407.0367","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-01T19:23:46Z","cross_cats_sorted":[],"title_canon_sha256":"f857fadaf2b1d994fa71c09d1472e9cd781024ce4027b6b0e6365ba4232af6f2","abstract_canon_sha256":"f12ac1ea69ddb03a6028323641837ffdd1f1cc1f233815fc319bf249e84faede"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:34.178851Z","signature_b64":"mCONtQx9WNOVnz+NxwjLIr+sDzpOUN7g21CUS0589mlSBtIYq93k5e7fIT+kd41zD6u7zuLChSpWOMkcc7+RDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"448792f0e95c250fdf2c3fb80f621175185410a5014442ca824ad803082bd5ca","last_reissued_at":"2026-05-18T02:48:34.178150Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:34.178150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Roman Bondage Number of Graphs on surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Vladimir Samodivkin","submitted_at":"2014-07-01T19:23:46Z","abstract_excerpt":"A Roman dominating function on a graph $G$ is a labeling $f : V(G) \\rightarrow \\{0, 1, 2\\}$ such that every vertex with label $0$ has a neighbor with label $2$. 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