{"paper":{"title":"Disjunctive Total Domination in Graphs","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":"2014-10-01T11:48:29Z","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 distance2 from it. The disjunctive total domination number, $\\gamma^d_t(G)$, is the minimum cardinality of such a set. We observe that $\\gamma^d_t(G) \\le \\gamma_t(G)$. We prove that if $G$ is a connected graph of order$n \\ge 8$, then $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0187","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"}