{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KMLGH5TET4BD6IMTPZQO3USCE3","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":"fc0870ff6e989c37d1f68615c6b1ff418c8cac29fc5eeb5075261df278512e32","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-02-05T07:05:35Z","title_canon_sha256":"5f583646c34102823c6b9a3b49921efd57f9246182fa19392839221fcc9dbef0"},"schema_version":"1.0","source":{"id":"1502.01442","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.01442","created_at":"2026-05-18T02:27:52Z"},{"alias_kind":"arxiv_version","alias_value":"1502.01442v1","created_at":"2026-05-18T02:27:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.01442","created_at":"2026-05-18T02:27:52Z"},{"alias_kind":"pith_short_12","alias_value":"KMLGH5TET4BD","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KMLGH5TET4BD6IMT","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KMLGH5TE","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:d66d765cc0087d27129003732a7350ffdf863613465aa32d508ce55014e29cb2","target":"graph","created_at":"2026-05-18T02:27:52Z","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":"In interconnection networks, matching preclusion is a measure of robustness when there is a link failure. Let $G$ be a graph of even order. The matching preclusion number $mp(G)$ is defined as the minimum number of edges whose deletion results in a subgraph without perfect matchings. Many interconnection networks are super matched, that is, their optimal matching preclusion sets are precisely those induced by a single vertex. In this paper, we obtain general results of vertex-transitive graphs including many known networks. A $k$-regular connected vertex-transitive graph has matching preclusio","authors_text":"Heping Zhang, Jinghua He, Qiuli Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-02-05T07:05:35Z","title":"Matching preclusion for vertex-transitive networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01442","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:cb806cd5531b9f90b6f12309298de76ae55e649861925c989feaeff0c7769505","target":"record","created_at":"2026-05-18T02:27:52Z","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":"fc0870ff6e989c37d1f68615c6b1ff418c8cac29fc5eeb5075261df278512e32","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-02-05T07:05:35Z","title_canon_sha256":"5f583646c34102823c6b9a3b49921efd57f9246182fa19392839221fcc9dbef0"},"schema_version":"1.0","source":{"id":"1502.01442","kind":"arxiv","version":1}},"canonical_sha256":"531663f6649f023f21937e60edd24226e738ebbb26ea1c99eace3d7d7494d4a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"531663f6649f023f21937e60edd24226e738ebbb26ea1c99eace3d7d7494d4a4","first_computed_at":"2026-05-18T02:27:52.044893Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:52.044893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IKn/xFo0slhALuXMosSBxDAPeJCUyH2wsN4wc65v8JYEIGBAxsqf0VzWrGw7TQpdkPPahP4RivISpisk4+xHDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:52.045512Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.01442","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb806cd5531b9f90b6f12309298de76ae55e649861925c989feaeff0c7769505","sha256:d66d765cc0087d27129003732a7350ffdf863613465aa32d508ce55014e29cb2"],"state_sha256":"0beae6cd44e2a5bcd4d5f42a4211da009589ce2ab2615b87d5c4bc931e628196"}