{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:YMJKXNWKEX3ZOFYZIEGOQWFRH2","short_pith_number":"pith:YMJKXNWK","schema_version":"1.0","canonical_sha256":"c312abb6ca25f7971719410ce858b13e98b9ee0007d5fa8674b0e8d0d74de13e","source":{"kind":"arxiv","id":"1008.3217","version":1},"attestation_state":"computed","paper":{"title":"On The Signed Edge Domination Number of Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Milad Siami, Pooya Hatami, Sadegh Bolouki, Saeed Akbari","submitted_at":"2010-08-19T04:59:59Z","abstract_excerpt":"Let $\\gamma'_s(G)$ be the signed edge domination number of G. In 2006, Xu conjectured that: for any $2$-connected graph G of order $ n (n \\geq 2),$ $\\gamma'_s(G)\\geq 1$. In this article we show that this conjecture is not true. More precisely, we show that for any positive integer $m$, there exists an $m$-connected graph $G$ such that $ \\gamma'_s(G)\\leq -\\frac{m}{6}|V(G)|.$ Also for every two natural numbers $m$ and $n$, we determine $\\gamma'_s(K_{m,n})$, where $K_{m,n}$ is the complete bipartite graph with part sizes $m$ and $n$."},"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":"1008.3217","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-08-19T04:59:59Z","cross_cats_sorted":[],"title_canon_sha256":"b3dabecc9eba7742583709bdda2fe6f41d8f09113b60466c74bd387fa4f04308","abstract_canon_sha256":"1dc37a1c6a8e03a32c83d1008c4b9ec299777d23c0d66b5b2bca086f45c3bb81"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:03.101040Z","signature_b64":"/Eh8VGhsqEDzmsvKn5X5cEycT2b8EnEih4rLwdu6ZI2WZ6WPYdsI8wBVpPEE9tGH5QoxvFRlTiJ4biTSDvN7Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c312abb6ca25f7971719410ce858b13e98b9ee0007d5fa8674b0e8d0d74de13e","last_reissued_at":"2026-05-18T04:42:03.100686Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:03.100686Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On The Signed Edge Domination Number of Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Milad Siami, Pooya Hatami, Sadegh Bolouki, Saeed Akbari","submitted_at":"2010-08-19T04:59:59Z","abstract_excerpt":"Let $\\gamma'_s(G)$ be the signed edge domination number of G. In 2006, Xu conjectured that: for any $2$-connected graph G of order $ n (n \\geq 2),$ $\\gamma'_s(G)\\geq 1$. In this article we show that this conjecture is not true. More precisely, we show that for any positive integer $m$, there exists an $m$-connected graph $G$ such that $ \\gamma'_s(G)\\leq -\\frac{m}{6}|V(G)|.$ Also for every two natural numbers $m$ and $n$, we determine $\\gamma'_s(K_{m,n})$, where $K_{m,n}$ is the complete bipartite graph with part sizes $m$ and $n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3217","kind":"arxiv","version":1},"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":"1008.3217","created_at":"2026-05-18T04:42:03.100743+00:00"},{"alias_kind":"arxiv_version","alias_value":"1008.3217v1","created_at":"2026-05-18T04:42:03.100743+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.3217","created_at":"2026-05-18T04:42:03.100743+00:00"},{"alias_kind":"pith_short_12","alias_value":"YMJKXNWKEX3Z","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_16","alias_value":"YMJKXNWKEX3ZOFYZ","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_8","alias_value":"YMJKXNWK","created_at":"2026-05-18T12:26:17.028572+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/YMJKXNWKEX3ZOFYZIEGOQWFRH2","json":"https://pith.science/pith/YMJKXNWKEX3ZOFYZIEGOQWFRH2.json","graph_json":"https://pith.science/api/pith-number/YMJKXNWKEX3ZOFYZIEGOQWFRH2/graph.json","events_json":"https://pith.science/api/pith-number/YMJKXNWKEX3ZOFYZIEGOQWFRH2/events.json","paper":"https://pith.science/paper/YMJKXNWK"},"agent_actions":{"view_html":"https://pith.science/pith/YMJKXNWKEX3ZOFYZIEGOQWFRH2","download_json":"https://pith.science/pith/YMJKXNWKEX3ZOFYZIEGOQWFRH2.json","view_paper":"https://pith.science/paper/YMJKXNWK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1008.3217&json=true","fetch_graph":"https://pith.science/api/pith-number/YMJKXNWKEX3ZOFYZIEGOQWFRH2/graph.json","fetch_events":"https://pith.science/api/pith-number/YMJKXNWKEX3ZOFYZIEGOQWFRH2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YMJKXNWKEX3ZOFYZIEGOQWFRH2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YMJKXNWKEX3ZOFYZIEGOQWFRH2/action/storage_attestation","attest_author":"https://pith.science/pith/YMJKXNWKEX3ZOFYZIEGOQWFRH2/action/author_attestation","sign_citation":"https://pith.science/pith/YMJKXNWKEX3ZOFYZIEGOQWFRH2/action/citation_signature","submit_replication":"https://pith.science/pith/YMJKXNWKEX3ZOFYZIEGOQWFRH2/action/replication_record"}},"created_at":"2026-05-18T04:42:03.100743+00:00","updated_at":"2026-05-18T04:42:03.100743+00:00"}