{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:45JGKYOFIUOY6JYVH7AI7TMLEY","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":"404d9930a4979454798c5fc15e3a3d18daf7551bbb8574235b7618c1549fdbb8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-03T13:34:41Z","title_canon_sha256":"4d5e32a2da3554014824dbd858fcddc94cc8b51e0d42a5aa4e92cbbf5b0bab1f"},"schema_version":"1.0","source":{"id":"1608.01189","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.01189","created_at":"2026-05-18T00:19:42Z"},{"alias_kind":"arxiv_version","alias_value":"1608.01189v2","created_at":"2026-05-18T00:19:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01189","created_at":"2026-05-18T00:19:42Z"},{"alias_kind":"pith_short_12","alias_value":"45JGKYOFIUOY","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"45JGKYOFIUOY6JYV","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"45JGKYOF","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:6a43986734aca0d45b94df16f8957e50ab033e2a35ca87390b0e2c3bc72eee9e","target":"graph","created_at":"2026-05-18T00:19:42Z","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 this paper, we give Nordhaus-Gaddum upper and lower bounds on the sum of the power propagation time of a graph and its complement, and we consider the effects of edge subdivisions and edge contractions on the power propagation time of a graph. We also study a generalization of power propagation time, known as $k-$power propagation time, by characterizing all simple graphs on $n$ vertices whose $k-$power propagation time is $n-1$ or $n-2$ (for $k\\geq 1$) and $n-3$ (for $k\\geq 2$). We determine all trees on $n$ vertices whose power propagation time ($k=1$) is $n-3$, and give partial character","authors_text":"Chassidy Bozeman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-03T13:34:41Z","title":"On the power propagation time of a graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01189","kind":"arxiv","version":2},"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":"sha256:9926b1839b4252b94f1dc58e03da22b10a7409fbea9917e830cc74c9ac4f1aa0","target":"record","created_at":"2026-05-18T00:19:42Z","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":"404d9930a4979454798c5fc15e3a3d18daf7551bbb8574235b7618c1549fdbb8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-03T13:34:41Z","title_canon_sha256":"4d5e32a2da3554014824dbd858fcddc94cc8b51e0d42a5aa4e92cbbf5b0bab1f"},"schema_version":"1.0","source":{"id":"1608.01189","kind":"arxiv","version":2}},"canonical_sha256":"e7526561c5451d8f27153fc08fcd8b26332ec58f5dd27bd09e697f43237c9917","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7526561c5451d8f27153fc08fcd8b26332ec58f5dd27bd09e697f43237c9917","first_computed_at":"2026-05-18T00:19:42.720748Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:42.720748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AFbb3QCkwAEaic3eJSRZRaMRA5senWDSacPMSx/WSwHhWcv7cLE5GXJOXwp7ET4DrKhGaXs6yjkesgdDw4CCBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:42.721381Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.01189","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9926b1839b4252b94f1dc58e03da22b10a7409fbea9917e830cc74c9ac4f1aa0","sha256:6a43986734aca0d45b94df16f8957e50ab033e2a35ca87390b0e2c3bc72eee9e"],"state_sha256":"fff39bb4cfe42f8d93932e36422a9feab14e2b492b42f897caf1cfd5f3827a65"}