{"paper":{"title":"On the power domination number of de Bruijn and Kautz digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Cyriac Grigorious, Joe Ryan, Sudeep Stephen, Thomas Kalinowski","submitted_at":"2016-12-06T09:35:17Z","abstract_excerpt":"Let $G=(V,A)$ be a directed graph without parallel arcs, and let $S\\subseteq V$ be a set of vertices. Let the sequence $S=S_0\\subseteq S_1\\subseteq S_2\\subseteq\\cdots$ be defined as follows: $S_1$ is obtained from $S_0$ by adding all out-neighbors of vertices in $S_0$. For $k\\geqslant 2$, $S_k$ is obtained from $S_{k-1}$ by adding all vertices $w$ such that for some vertex $v\\in S_{k-1}$, $w$ is the unique out-neighbor of $v$ in $V\\setminus S_{k-1}$. We set $M(S)=S_0\\cup S_1\\cup\\cdots$, and call $S$ a \\emph{power dominating set} for $G$ if $M(S)=V(G)$. The minimum cardinality of such a set is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01721","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"}