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It is conjectured that the domination polynomial of any graph is unimodal.\nIn this paper we present  some  families of graphs whose domination polynomials are unimodal."},"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":"1401.1159","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-06T18:05:12Z","cross_cats_sorted":[],"title_canon_sha256":"e971907a28a1b065ac3aad57d990d0d1bd4f74adc1618f2d65bbe1768148440b","abstract_canon_sha256":"d57c648110710f37c6c516ff12d1660b215c7d35d2b5fc1b67644fa267b0511f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:56.673508Z","signature_b64":"JTkwGiSmGZ+IZgXtIUinqvgUTRuKTzmvBO/OV/mhz58T+1ux2cQuQTju+QhC9s5L6ezRwEiHe9NKjZISZ38kBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"733da6376780276fb0309a38658f6fd2b148b05b8a9fa49dab1d8d908beda3c6","last_reissued_at":"2026-05-18T03:02:56.672970Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:56.672970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some families of graphs whose domination polynomials are unimodal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Saeid Alikhani, Somayeh Jahari","submitted_at":"2014-01-06T18:05:12Z","abstract_excerpt":"Let $G$ be a simple graph of order $n$.\nThe domination polynomial of $G$ is the polynomial\n$D(G, x)=\\sum_{i=\\gamma(G)}^{n} d(G,i) x^{i}$,\nwhere $d(G,i)$ is the number of dominating sets of $G$ of size $i$ and\n$\\gamma(G)$ is the domination number of $G$.  It is conjectured that the domination polynomial of any graph is unimodal.\nIn this paper we present  some  families of graphs whose domination polynomials are unimodal."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1159","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1401.1159","created_at":"2026-05-18T03:02:56.673047+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.1159v2","created_at":"2026-05-18T03:02:56.673047+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.1159","created_at":"2026-05-18T03:02:56.673047+00:00"},{"alias_kind":"pith_short_12","alias_value":"OM62MN3HQATW","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_16","alias_value":"OM62MN3HQATW7MBQ","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_8","alias_value":"OM62MN3H","created_at":"2026-05-18T12:28:41.024544+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OM62MN3HQATW7MBQTI4GLD3P2K","json":"https://pith.science/pith/OM62MN3HQATW7MBQTI4GLD3P2K.json","graph_json":"https://pith.science/api/pith-number/OM62MN3HQATW7MBQTI4GLD3P2K/graph.json","events_json":"https://pith.science/api/pith-number/OM62MN3HQATW7MBQTI4GLD3P2K/events.json","paper":"https://pith.science/paper/OM62MN3H"},"agent_actions":{"view_html":"https://pith.science/pith/OM62MN3HQATW7MBQTI4GLD3P2K","download_json":"https://pith.science/pith/OM62MN3HQATW7MBQTI4GLD3P2K.json","view_paper":"https://pith.science/paper/OM62MN3H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.1159&json=true","fetch_graph":"https://pith.science/api/pith-number/OM62MN3HQATW7MBQTI4GLD3P2K/graph.json","fetch_events":"https://pith.science/api/pith-number/OM62MN3HQATW7MBQTI4GLD3P2K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OM62MN3HQATW7MBQTI4GLD3P2K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OM62MN3HQATW7MBQTI4GLD3P2K/action/storage_attestation","attest_author":"https://pith.science/pith/OM62MN3HQATW7MBQTI4GLD3P2K/action/author_attestation","sign_citation":"https://pith.science/pith/OM62MN3HQATW7MBQTI4GLD3P2K/action/citation_signature","submit_replication":"https://pith.science/pith/OM62MN3HQATW7MBQTI4GLD3P2K/action/replication_record"}},"created_at":"2026-05-18T03:02:56.673047+00:00","updated_at":"2026-05-18T03:02:56.673047+00:00"}