{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:VO2QSNNYW4ADIZPBHY4NU6YXNE","short_pith_number":"pith:VO2QSNNY","schema_version":"1.0","canonical_sha256":"abb50935b8b7003465e13e38da7b17692086a6b80f0e43e17c9cde258f64727e","source":{"kind":"arxiv","id":"1510.08749","version":1},"attestation_state":"computed","paper":{"title":"Bounds on the Exponential Domination Number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dieter Rautenbach, Pascal Ochem, Stephane Bessy","submitted_at":"2015-10-29T15:52:09Z","abstract_excerpt":"As a natural variant of domination in graphs, Dankelmann et al. [Domination with exponential decay, Discrete Math. 309 (2009) 5877-5883] introduce exponential domination, where vertices are considered to have some dominating power that decreases exponentially with the distance, and the dominated vertices have to accumulate a sufficient amount of this power emanating from the dominating vertices. More precisely, if $S$ is a set of vertices of a graph $G$, then $S$ is an exponential dominating set of $G$ if $\\sum\\limits_{v\\in S}\\left(\\frac{1}{2}\\right)^{{\\rm dist}_{(G,S)}(u,v)-1}\\geq 1$ for ever"},"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":"1510.08749","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-29T15:52:09Z","cross_cats_sorted":[],"title_canon_sha256":"2358513b330bfaeef3b94709d4d9b21f61c95b96ad6372370ef0f877746fbde7","abstract_canon_sha256":"76f679947d4c8903ea01711fe8a2fb0a0bb36fb5a6976a885008b1b1160e06d6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:26.885189Z","signature_b64":"Rq7grl63kFQ9LLPcjSY67qOQBhdO6IDkdmb1jNtRJqD3gTPHFHSZbFbi4KoPVSwrYnPrslR4FbeCMlF8do08BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"abb50935b8b7003465e13e38da7b17692086a6b80f0e43e17c9cde258f64727e","last_reissued_at":"2026-05-18T01:28:26.884495Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:26.884495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounds on the Exponential Domination Number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dieter Rautenbach, Pascal Ochem, Stephane Bessy","submitted_at":"2015-10-29T15:52:09Z","abstract_excerpt":"As a natural variant of domination in graphs, Dankelmann et al. [Domination with exponential decay, Discrete Math. 309 (2009) 5877-5883] introduce exponential domination, where vertices are considered to have some dominating power that decreases exponentially with the distance, and the dominated vertices have to accumulate a sufficient amount of this power emanating from the dominating vertices. More precisely, if $S$ is a set of vertices of a graph $G$, then $S$ is an exponential dominating set of $G$ if $\\sum\\limits_{v\\in S}\\left(\\frac{1}{2}\\right)^{{\\rm dist}_{(G,S)}(u,v)-1}\\geq 1$ for ever"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08749","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":"1510.08749","created_at":"2026-05-18T01:28:26.884601+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.08749v1","created_at":"2026-05-18T01:28:26.884601+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.08749","created_at":"2026-05-18T01:28:26.884601+00:00"},{"alias_kind":"pith_short_12","alias_value":"VO2QSNNYW4AD","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_16","alias_value":"VO2QSNNYW4ADIZPB","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_8","alias_value":"VO2QSNNY","created_at":"2026-05-18T12:29:47.479230+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/VO2QSNNYW4ADIZPBHY4NU6YXNE","json":"https://pith.science/pith/VO2QSNNYW4ADIZPBHY4NU6YXNE.json","graph_json":"https://pith.science/api/pith-number/VO2QSNNYW4ADIZPBHY4NU6YXNE/graph.json","events_json":"https://pith.science/api/pith-number/VO2QSNNYW4ADIZPBHY4NU6YXNE/events.json","paper":"https://pith.science/paper/VO2QSNNY"},"agent_actions":{"view_html":"https://pith.science/pith/VO2QSNNYW4ADIZPBHY4NU6YXNE","download_json":"https://pith.science/pith/VO2QSNNYW4ADIZPBHY4NU6YXNE.json","view_paper":"https://pith.science/paper/VO2QSNNY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.08749&json=true","fetch_graph":"https://pith.science/api/pith-number/VO2QSNNYW4ADIZPBHY4NU6YXNE/graph.json","fetch_events":"https://pith.science/api/pith-number/VO2QSNNYW4ADIZPBHY4NU6YXNE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VO2QSNNYW4ADIZPBHY4NU6YXNE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VO2QSNNYW4ADIZPBHY4NU6YXNE/action/storage_attestation","attest_author":"https://pith.science/pith/VO2QSNNYW4ADIZPBHY4NU6YXNE/action/author_attestation","sign_citation":"https://pith.science/pith/VO2QSNNYW4ADIZPBHY4NU6YXNE/action/citation_signature","submit_replication":"https://pith.science/pith/VO2QSNNYW4ADIZPBHY4NU6YXNE/action/replication_record"}},"created_at":"2026-05-18T01:28:26.884601+00:00","updated_at":"2026-05-18T01:28:26.884601+00:00"}