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A set $S$ of vertices in $G$ is a disjunctive total dominating set of $G$ if every vertex is adjacent to a vertex of $S$ or has at least two vertices in $S$ at distance $2$ from it. The disjunctive total domination number, $\\gamma^d_t(G)$, is the minimum cardinality of such a set. We observe that $\\gamma^d_t(G) \\le \\gamma_t(G)$. Let $G$ be a connected graph on $n$ vertices with minimum degree"},"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":"1409.1681","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-09-05T07:46:34Z","cross_cats_sorted":[],"title_canon_sha256":"5624eb31dac712f6b0a2d8571c64e13e873d643eeafc3fd5c48cd5f9144c0c02","abstract_canon_sha256":"e26cc60e21d8e1fbe72305cb65e53adc43da25d502ca22d1c95565a5356450e5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:45.823785Z","signature_b64":"IFFagntuXn0ZdTLXyvSotVF+kAEI7FwGfaheg+BsExSfjJgfQrVDiEBgwqV2WBahr8ffFIrxyxxmP3RdJEHHCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0eb5e73d2046e7448fab01b166c6b3b2e3ca976c8e47594904288e7807dea76","last_reissued_at":"2026-05-18T02:38:45.823353Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:45.823353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Graphs with Large Disjunctive Total Domination Number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Michael A. Henning, Viroshan Naicker","submitted_at":"2014-09-05T07:46:34Z","abstract_excerpt":"Let $G$ be a graph with no isolated vertex. In this paper, we study a parameter that is a relaxation of arguably the most important domination parameter, namely the total domination number, $\\gamma_t(G)$. A set $S$ of vertices in $G$ is a disjunctive total dominating set of $G$ if every vertex is adjacent to a vertex of $S$ or has at least two vertices in $S$ at distance $2$ from it. The disjunctive total domination number, $\\gamma^d_t(G)$, is the minimum cardinality of such a set. We observe that $\\gamma^d_t(G) \\le \\gamma_t(G)$. 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