{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:L5XOKPH55I3TJVATWVCLVRNYCK","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8dcef9ef53622fbf48ec430ea06f3793c753640a1e6e2cbf2ea0c7c560a2782a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-23T16:53:22Z","title_canon_sha256":"3ee404d1d246a586bd9ee9be53c698269d78bc9f6c859e69bc1aa369a90e941d"},"schema_version":"1.0","source":{"id":"1809.08630","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.08630","created_at":"2026-05-18T00:05:03Z"},{"alias_kind":"arxiv_version","alias_value":"1809.08630v1","created_at":"2026-05-18T00:05:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.08630","created_at":"2026-05-18T00:05:03Z"},{"alias_kind":"pith_short_12","alias_value":"L5XOKPH55I3T","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"L5XOKPH55I3TJVAT","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"L5XOKPH5","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:c416c9fb42c57dabbb53af9495c82162e8815146a12348ff18222eb9cacd1c33","target":"graph","created_at":"2026-05-18T00:05:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The aim of this work is to investigate the nonnegative signed domination number $\\gamma^{NN}_s$ with emphasis on regular, ($r+1$)-clique-free graphs and trees. We give lower and upper bounds on $\\gamma^{NN}_s$ for regular graphs and prove that $n/3$ is the best possible upper bound on this parameter for a cubic graph of order $n$, specifically. As an application of the classic theorem of Tur\\'{a}n we bound $\\gamma^{NN}_s(G)$ from below, for an ($r+1$)-clique-free graph $G$ and characterize all such graphs for which the equality holds, which corrects and generalizes a result for bipartite graph","authors_text":"Babak Samadi, Doost Ali Mojdeh, Lutz Volkmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-23T16:53:22Z","title":"Bounds on the nonnegative signed domination number of graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08630","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:9ed9746f68f583c96cb43e1b234eaeb4419d30479e60256abfb13b66f84b9e07","target":"record","created_at":"2026-05-18T00:05:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8dcef9ef53622fbf48ec430ea06f3793c753640a1e6e2cbf2ea0c7c560a2782a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-23T16:53:22Z","title_canon_sha256":"3ee404d1d246a586bd9ee9be53c698269d78bc9f6c859e69bc1aa369a90e941d"},"schema_version":"1.0","source":{"id":"1809.08630","kind":"arxiv","version":1}},"canonical_sha256":"5f6ee53cfdea3734d413b544bac5b8129044b6201914405a5579895eb064fe79","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f6ee53cfdea3734d413b544bac5b8129044b6201914405a5579895eb064fe79","first_computed_at":"2026-05-18T00:05:03.949355Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:03.949355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3iNf+eczdxE6BSeoe2K+Pji6m+1iRMvgfoGo/KQQiFWqpcqVQBumIl0Y7f5ypS4A07oC0WO4TN+ClmfgFawhAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:03.949943Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.08630","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ed9746f68f583c96cb43e1b234eaeb4419d30479e60256abfb13b66f84b9e07","sha256:c416c9fb42c57dabbb53af9495c82162e8815146a12348ff18222eb9cacd1c33"],"state_sha256":"6cce5208c28a146bcc4abb9d020f17809253050e8f91c8bd16594245b5716f61"}