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The minimum cardinality of an $(a,b)$-dominating set of $G$ is the $(a,b)$-domination number of $G$, denoted by $\\gamma_{a,b}(G)$. There are various results about upper bounds for $\\gamma_{a,b}(G)$ when $G$ is regular or $a$ and $b$ are small numbers.\n  In the first part of this paper, for a given graph $G$ with the minimum degree o"},"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":"1803.04031","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-11T20:10:07Z","cross_cats_sorted":[],"title_canon_sha256":"14e67526e97d614983137b21530cc2a99eeeb0259e409a37b6b57f8b012696cd","abstract_canon_sha256":"dffe14f11443ffe580ac8a5e025a94e7952f25071424d3248848de8855452692"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:33.147769Z","signature_b64":"QuxphhOicZLRy9/UA5KHv+IqAvkxTXhU4XTzm2Amw4oMWN0GuVTpZRep7dl5lFmsQ3x8jvnT2HGiK0HbAGY/Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd43964f13d4561424e38aa016946eb55650467370899f5ce54e1dfbaded8465","last_reissued_at":"2026-05-18T00:21:33.147115Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:33.147115Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Upper bounds for domination numbers of graphs using Tur\\'an's Theorem and Lov\\'asz local lemma","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Amir Jafari, Sharareh Alipour","submitted_at":"2018-03-11T20:10:07Z","abstract_excerpt":"Let $G$ be a connected graph of order $n$ with vertex set $V(G)$. 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