{"paper":{"title":"On graphs with equal total domination and Grundy total domination number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Marko Jakovac, Tanja Gologranc, Tilen Marc, Tim Kos","submitted_at":"2019-06-28T14:18:06Z","abstract_excerpt":"A sequence $(v_1,\\ldots ,v_k)$ of vertices in a graph $G$ without isolated vertices is called a total dominating sequence if every vertex $v_i$ in the sequence totally dominates at least one vertex that was not totally dominated by $\\{v_1,\\ldots , v_{i-1}\\}$ and $\\{v_1,\\ldots ,v_k\\}$ is a total dominating set of $G$. The length of a shortest such sequence is the total domination number of G ($\\gamma_t(G)$), while the length of a longest such sequence is the Grundy total domination number of $G$ ($\\gamma_{gr}^t(G)$). In this paper we study graphs with equal total and Grundy total domination num"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.12235","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"}