{"paper":{"title":"On the equality of domination number and $ 2 $-domination number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Csilla Bujt\\'as, G\\\"ulnaz Boruzanl{\\i} Ekinci","submitted_at":"2019-07-18T03:59:36Z","abstract_excerpt":"The 2-domination number $\\gamma_2(G)$ of a graph $G$ is the minimum cardinality of a set $ D \\subseteq V(G) $ for which every vertex outside $ D $ is adjacent to at least two vertices in $ D $. Clearly, $ \\gamma_2(G) $ cannot be smaller than the domination number $ \\gamma(G) $. We consider a large class of graphs and characterize those members which satisfy $\\gamma_2=\\gamma$. For the general case, we prove that it is NP-hard to decide whether $\\gamma_2=\\gamma$ holds. We also give a necessary and sufficient condition for a graph to satisfy the equality hereditarily."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.07866","kind":"arxiv","version":2},"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/1907.07866/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"}