{"paper":{"title":"On the disjunctive domination numbers of the torus grid graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Zhi Qiao","submitted_at":"2026-05-19T07:51:05Z","abstract_excerpt":"Let $\\Gamma=(V,E)$ be a graph. A disjunctive dominating set in $\\Gamma$ is a set $S\\subseteq V$ such that every vertex not in $S$ is adjacent to a vertex of $S$, or has at least two vertices in $S$ at distance $2$ from it.\n  The minimum cardinality of a disjunctive dominating set in $\\Gamma$ is called the disjunctive domination number of $\\Gamma$.\n  In this paper, we give bounds for the disjunctive domination numbers of the torus grid graphs $C_m\\Box C_n$, and determine the disjunctive domination numbers of $C_3\\Box C_n$ and $C_4\\Box C_n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19497","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.19497/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}