{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:COZSEL2DY476X2OF3FLG4ORIMT","short_pith_number":"pith:COZSEL2D","canonical_record":{"source":{"id":"1905.11254","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-24T15:28:45Z","cross_cats_sorted":[],"title_canon_sha256":"83b38af65524897073b960db9ac028a4a1fe26ca4a90d0a9a5b46f5d19f5c815","abstract_canon_sha256":"5b350d0d0502203a2801c419588c8c64fe9e0846b78fe972bb3c8355735b5982"},"schema_version":"1.0"},"canonical_sha256":"13b3222f43c73febe9c5d9566e3a2864c68c50084a1bcee447a1d911cb684d2d","source":{"kind":"arxiv","id":"1905.11254","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.11254","created_at":"2026-05-17T23:45:02Z"},{"alias_kind":"arxiv_version","alias_value":"1905.11254v1","created_at":"2026-05-17T23:45:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.11254","created_at":"2026-05-17T23:45:02Z"},{"alias_kind":"pith_short_12","alias_value":"COZSEL2DY476","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"COZSEL2DY476X2OF","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"COZSEL2D","created_at":"2026-05-18T12:33:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:COZSEL2DY476X2OF3FLG4ORIMT","target":"record","payload":{"canonical_record":{"source":{"id":"1905.11254","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-24T15:28:45Z","cross_cats_sorted":[],"title_canon_sha256":"83b38af65524897073b960db9ac028a4a1fe26ca4a90d0a9a5b46f5d19f5c815","abstract_canon_sha256":"5b350d0d0502203a2801c419588c8c64fe9e0846b78fe972bb3c8355735b5982"},"schema_version":"1.0"},"canonical_sha256":"13b3222f43c73febe9c5d9566e3a2864c68c50084a1bcee447a1d911cb684d2d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:02.557117Z","signature_b64":"YiUwL9cI3JJLOAw+Dp7RcDEojBuc5ZfyiYnmmoND4Xchm63Ze8jRqg64crzMCi5xyt23sOT9pPVXTiJ8hLTLBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13b3222f43c73febe9c5d9566e3a2864c68c50084a1bcee447a1d911cb684d2d","last_reissued_at":"2026-05-17T23:45:02.556621Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:02.556621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.11254","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:45:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yV6qmOn1QxFcUYsZrtEgCapWp8M14EvleGnHGiPSNabbxI9JmALwNw2GuK+Ut3BQbF5WgnYXIKeR+5FYLuPlBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T09:21:30.277691Z"},"content_sha256":"7ddc92fe2f63c62719d40e31b7dfd383372af7d7641e591c405e97837520d621","schema_version":"1.0","event_id":"sha256:7ddc92fe2f63c62719d40e31b7dfd383372af7d7641e591c405e97837520d621"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:COZSEL2DY476X2OF3FLG4ORIMT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the $g$-good-neighbor connectivity of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jichang Wu, Sun-Yuan Hsieh, Yaping Mao, Zhao Wang","submitted_at":"2019-05-24T15:28:45Z","abstract_excerpt":"Connectivity and diagnosability are two important parameters for the fault tolerant of an interconnection network $G$. In 1996, F\\`{a}brega and Fiol proposed the $g$-good-neighbor connectivity of $G$. In this paper, we show that $1\\leq \\kappa^g(G)\\leq n-2g-2$ for $0\\leq g\\leq \\left\\{\\Delta(G),\\left\\lfloor \\frac{n-3}{2}\\right\\rfloor\\right\\}$, and graphs with $\\kappa^g(G)=1,2$ and trees with $\\kappa^g(T_n)=n-t$ for $4\\leq t\\leq \\frac{n+2}{2}$ are characterized, respectively. In the end, we get the three extremal results for the $g$-good-neighbor connectivity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.11254","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:45:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"doRrjhOn+L3f01U5f5LX6M2maPmhsnRatwEeKVY3u3WyLTWyUoSR2yCR9myWv9n81yUtQErDeP24IWZE9dAhDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T09:21:30.278414Z"},"content_sha256":"b42057a1e6b4da1c26ce199f57777bae86ffecb3394ab6a6f46f12f7c426f61a","schema_version":"1.0","event_id":"sha256:b42057a1e6b4da1c26ce199f57777bae86ffecb3394ab6a6f46f12f7c426f61a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/COZSEL2DY476X2OF3FLG4ORIMT/bundle.json","state_url":"https://pith.science/pith/COZSEL2DY476X2OF3FLG4ORIMT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/COZSEL2DY476X2OF3FLG4ORIMT/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T09:21:30Z","links":{"resolver":"https://pith.science/pith/COZSEL2DY476X2OF3FLG4ORIMT","bundle":"https://pith.science/pith/COZSEL2DY476X2OF3FLG4ORIMT/bundle.json","state":"https://pith.science/pith/COZSEL2DY476X2OF3FLG4ORIMT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/COZSEL2DY476X2OF3FLG4ORIMT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:COZSEL2DY476X2OF3FLG4ORIMT","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":"5b350d0d0502203a2801c419588c8c64fe9e0846b78fe972bb3c8355735b5982","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-24T15:28:45Z","title_canon_sha256":"83b38af65524897073b960db9ac028a4a1fe26ca4a90d0a9a5b46f5d19f5c815"},"schema_version":"1.0","source":{"id":"1905.11254","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.11254","created_at":"2026-05-17T23:45:02Z"},{"alias_kind":"arxiv_version","alias_value":"1905.11254v1","created_at":"2026-05-17T23:45:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.11254","created_at":"2026-05-17T23:45:02Z"},{"alias_kind":"pith_short_12","alias_value":"COZSEL2DY476","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"COZSEL2DY476X2OF","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"COZSEL2D","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:b42057a1e6b4da1c26ce199f57777bae86ffecb3394ab6a6f46f12f7c426f61a","target":"graph","created_at":"2026-05-17T23:45:02Z","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":"Connectivity and diagnosability are two important parameters for the fault tolerant of an interconnection network $G$. In 1996, F\\`{a}brega and Fiol proposed the $g$-good-neighbor connectivity of $G$. In this paper, we show that $1\\leq \\kappa^g(G)\\leq n-2g-2$ for $0\\leq g\\leq \\left\\{\\Delta(G),\\left\\lfloor \\frac{n-3}{2}\\right\\rfloor\\right\\}$, and graphs with $\\kappa^g(G)=1,2$ and trees with $\\kappa^g(T_n)=n-t$ for $4\\leq t\\leq \\frac{n+2}{2}$ are characterized, respectively. In the end, we get the three extremal results for the $g$-good-neighbor connectivity.","authors_text":"Jichang Wu, Sun-Yuan Hsieh, Yaping Mao, Zhao Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-24T15:28:45Z","title":"On the $g$-good-neighbor connectivity of graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.11254","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":"sha256:7ddc92fe2f63c62719d40e31b7dfd383372af7d7641e591c405e97837520d621","target":"record","created_at":"2026-05-17T23:45:02Z","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":"5b350d0d0502203a2801c419588c8c64fe9e0846b78fe972bb3c8355735b5982","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-24T15:28:45Z","title_canon_sha256":"83b38af65524897073b960db9ac028a4a1fe26ca4a90d0a9a5b46f5d19f5c815"},"schema_version":"1.0","source":{"id":"1905.11254","kind":"arxiv","version":1}},"canonical_sha256":"13b3222f43c73febe9c5d9566e3a2864c68c50084a1bcee447a1d911cb684d2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13b3222f43c73febe9c5d9566e3a2864c68c50084a1bcee447a1d911cb684d2d","first_computed_at":"2026-05-17T23:45:02.556621Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:02.556621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YiUwL9cI3JJLOAw+Dp7RcDEojBuc5ZfyiYnmmoND4Xchm63Ze8jRqg64crzMCi5xyt23sOT9pPVXTiJ8hLTLBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:02.557117Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.11254","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ddc92fe2f63c62719d40e31b7dfd383372af7d7641e591c405e97837520d621","sha256:b42057a1e6b4da1c26ce199f57777bae86ffecb3394ab6a6f46f12f7c426f61a"],"state_sha256":"eb00c682f194d543e0af9ae51893b4ec11ed090c66947a7da09329de3f479445"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aRlDesbFegi01eVLq5q6quAwVdP5cXgadfy/22CF4x7mL8CzzjVF0WxhubEPfJsfSc6QlG05s2IMJ0tMbOjaBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T09:21:30.282586Z","bundle_sha256":"aa02aff0cf4896c80118daa5bc6375459702ed4f21e34ce38170dcd4ee2690a3"}}